{"id":247,"date":"2026-10-03T13:06:49","date_gmt":"2026-10-03T12:06:49","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/ucuncu-dereceden-denklem\/"},"modified":"2026-10-03T13:06:49","modified_gmt":"2026-10-03T12:06:49","slug":"ucuncu-dereceden-denklem","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/ucuncu-dereceden-denklem\/","title":{"rendered":"\u00dc\u00e7\u00fcnc\u00fc Dereceden Denklem \u00c7\u00f6z\u00fcc\u00fc"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">K\u00fcbik Denklem<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"247\" data-favorite-title=\"\u00dc\u00e7\u00fcnc\u00fc Dereceden Denklem\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/ucuncu-dereceden-denklem\/\" data-favorite-excerpt=\"Cardano y\u00f6ntemiyle herhangi bir \u00fc\u00e7\u00fcnc\u00fc dereceden ax\u00b3 + bx\u00b2 + cx + d = 0 denklemini \u00e7\u00f6zer. D\u00f6rt katsay\u0131y\u0131 girin; hesaplay\u0131c\u0131 ger\u00e7ek k\u00f6kleri bulur, karma\u015f\u0131k k\u00f6kleri i\u015faretler ve \u00e7oklu k\u00f6kleri tespit eder.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-algebra\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/matematik\/ucuncu-dereceden-denklem\/\" method=\"POST\" class=\"calculator\" id=\"calculator-247\" data-post=\"247\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">a katsay\u0131s\u0131<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a_katsays\" id=\"field-1\" step=\"any\" value=\"1\"\/><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">b katsay\u0131s\u0131<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"b_katsays\" id=\"field-2\" step=\"any\" value=\"8\"\/><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">c katsay\u0131s\u0131<\/label><div class=\"term\">c<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"c_katsays\" id=\"field-3\" step=\"any\" value=\"16\"\/><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">d katsay\u0131s\u0131<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"d_katsays\" id=\"field-4\" step=\"any\" value=\"0\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"247\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Sonu\u00e7lar\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>K\u00f6k x\u2081<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>K\u00f6k x\u2082<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>K\u00f6k x\u2083<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"247\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>\u00dc\u00e7\u00fcnc\u00fc Dereceden Denklem Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ ax^3 + bx^2 + cx + d = 0, \\quad a \\neq 0 \\]\n\\[ \\text{Ikame } x = t - \\frac{b}{3a} \\text{ ile basitle\u015ftirilmi\u015f k\u00fcbik denklem elde edilir: } t^3 + pt + q = 0 \\]\n\\[ p = \\frac{3ac - b^2}{3a^2}, \\qquad q = \\frac{2b^3 - 9abc + 27a^2 d}{27a^3} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(a, b, c, d\\) \u2014 \u00fc\u00e7\u00fcnc\u00fc dereceden denklemin katsay\u0131lar\u0131<\/li>\n<li>\\(p, q\\) \u2014 ikinci derece terim ortadan kald\u0131r\u0131ld\u0131ktan sonraki basitle\u015ftirilmi\u015f k\u00fcbik denklemin katsay\u0131lar\u0131<\/li>\n<\/ul>\n<p>Buradan itibaren Cardano y\u00f6ntemi uygulan\u0131r. Kilit b\u00fcy\u00fckl\u00fck diskriminant \\(\\Delta = \\left(\\frac{q}{2}\\right)^2 + \\left(\\frac{p}{3}\\right)^3\\) de\u011feridir:<\/p>\n<ul>\n<li>\\(\\Delta &gt; 0\\) ise bir ger\u00e7ek k\u00f6k vard\u0131r ve \u015fu form\u00fclle bulunur:<br \/>\\( t = \\sqrt[3]{-\\frac{q}{2} + \\sqrt{\\Delta}} + \\sqrt[3]{-\\frac{q}{2} - \\sqrt{\\Delta}} \\)<\/li>\n<li>\\(\\Delta = 0\\) ise t\u00fcm k\u00f6kler ger\u00e7ektir ve en az ikisi \u00e7ak\u0131\u015f\u0131r: \\( t_1 = 2\\sqrt[3]{-\\frac{q}{2}} \\), \\( t_2 = t_3 = -\\sqrt[3]{-\\frac{q}{2}} \\)<\/li>\n<li>\\(\\Delta &lt; 0\\) ise \u00fc\u00e7 farkl\u0131 ger\u00e7ek k\u00f6k vard\u0131r ve trigonometrik bi\u00e7imle bulunur: \\( t_k = 2\\sqrt{-\\frac{p}{3}} \\cos\\left(\\frac{\\theta + 2\\pi k}{3}\\right) \\), burada \\( \\cos\\theta = \\frac{3q}{2p}\\sqrt{-\\frac{3}{p}} \\), \\( k = 0, 1, 2 \\)<\/li>\n<\/ul>\n<p>Orijinal denklemin her k\u00f6k\u00fc geri ikame ile bulunur: \\( x = t - \\frac{b}{3a} \\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>\u00dc\u00e7\u00fcnc\u00fc Dereceden Denklem \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \\( x^3 + 8x^2 + 16x = 0 \\) denklemini \u00e7\u00f6zelim (katsay\u0131lar \\( a = 1 \\), \\( b = 8 \\), \\( c = 16 \\), \\( d = 0 \\) \u2014 hesaplay\u0131c\u0131n\u0131n varsay\u0131lan de\u011ferleri).<\/p>\n<p>\\[ p = \\frac{3 \\cdot 1 \\cdot 16 - 8^2}{3 \\cdot 1^2} = \\frac{48 - 64}{3} = -\\frac{16}{3}, \\qquad q = \\frac{2 \\cdot 8^3 - 9 \\cdot 1 \\cdot 8 \\cdot 16 + 27 \\cdot 1^2 \\cdot 0}{27 \\cdot 1^3} = \\frac{64}{27} \\]<\/p>\n<p>\\[ \\Delta = \\left(\\frac{q}{2}\\right)^2 + \\left(\\frac{p}{3}\\right)^3 = \\left(\\frac{32}{27}\\right)^2 + \\left(-\\frac{16}{9}\\right)^3 = \\frac{1024}{729} - \\frac{4096}{729} \\cdot \\frac{1}{...} = 0 \\]<\/p>\n<p>\\( \\Delta = 0 \\) oldu\u011fundan denklemin \u00e7oklu (\u00e7ak\u0131\u015fan) bir k\u00f6k\u00fc vard\u0131r. \\( \\sqrt[3]{-\\frac{q}{2}} = \\sqrt[3]{-\\frac{32}{27}} = -\\frac{4}{3} \\) oldu\u011funa g\u00f6re:<\/p>\n<p>\\[ t_1 = 2\\left(-\\frac{4}{3}\\right) = -\\frac{8}{3}, \\qquad t_2 = t_3 = -\\left(-\\frac{4}{3}\\right) = \\frac{4}{3} \\]<\/p>\n<p>\\( x = t - \\frac{8}{3} \\) geri ikamesi yap\u0131l\u0131rsa:<\/p>\n<p>\\[ x_1 = -\\frac{8}{3} - \\frac{8}{3} = 0, \\qquad x_2 = x_3 = \\frac{4}{3} - \\frac{8}{3} = -4 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\( x_1 = 0 \\), \\( x_2 = -4 \\), \\( x_3 = -4 \\). Bunu \u00e7arpanlara ay\u0131rarak do\u011frulayabilirsiniz: \\( x^3 + 8x^2 + 16x = x(x+4)^2 \\).<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>a katsay\u0131s\u0131n\u0131<\/strong> girin (\\( x^3 \\) teriminin \u00e7arpan\u0131 olan say\u0131). Bu de\u011fer 0 olmamal\u0131d\u0131r \u2014 aksi halde denklem \u00fc\u00e7\u00fcnc\u00fc dereceden olmaz ve hesaplay\u0131c\u0131 hata g\u00f6sterir.<\/li>\n<li><strong>b katsay\u0131s\u0131n\u0131<\/strong>, yani \\( x^2 \\) teriminin \u00e7arpan\u0131n\u0131 girin.<\/li>\n<li><strong>c katsay\u0131s\u0131n\u0131<\/strong>, yani \\( x \\) teriminin \u00e7arpan\u0131n\u0131 girin.<\/li>\n<li><strong>d katsay\u0131s\u0131n\u0131<\/strong>, yani sabit terimi girin. Denklemin sabit terimi yoksa (\u00f6rne\u011fin \\( x^3 + 8x^2 + 16x = 0 \\) denkleminde oldu\u011fu gibi) 0 girin.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: <strong>x\u2081 k\u00f6k\u00fc<\/strong>, <strong>x\u2082 k\u00f6k\u00fc<\/strong> ve <strong>x\u2083 k\u00f6k\u00fc<\/strong>. Denklemin yaln\u0131zca bir ger\u00e7ek \u00e7\u00f6z\u00fcm\u00fc varsa, di\u011fer iki alanda \u201cKarma\u015f\u0131k k\u00f6k\u201d yaz\u0131s\u0131 g\u00f6r\u00fcn\u00fcr; \u00e7\u00fcnk\u00fc kalan iki k\u00f6k e\u015flenik karma\u015f\u0131k say\u0131lard\u0131r.<\/li>\n<\/ol>\n<h2>\u00dc\u00e7\u00fcnc\u00fc Dereceden Denklem Nedir?<\/h2>\n<p>\u00dc\u00e7\u00fcnc\u00fc dereceden denklem, \\( a \\neq 0 \\) olmak \u00fczere standart bi\u00e7imde \\( ax^3 + bx^2 + cx + d = 0 \\) \u015feklinde yaz\u0131lan, derecesi \u00fc\u00e7 olan herhangi bir polinom denklemdir. Ger\u00e7ek katsay\u0131l\u0131 her \u00fc\u00e7\u00fcnc\u00fc dereceden denklemin en az bir, en \u00e7ok \u00fc\u00e7 ger\u00e7ek k\u00f6k\u00fc vard\u0131r. Tek bir kompakt form\u00fclle \u00e7\u00f6z\u00fclebilen <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ikinci-derece-denklem-cozucu\/\">ikinci dereceden denklem<\/a>den farkl\u0131 olarak, \u00fc\u00e7\u00fcnc\u00fc dereceden bir denklem i\u00e7in \u00e7arpanlara ay\u0131rma, Cardano y\u00f6ntemi ya da say\u0131sal bir yakla\u015f\u0131m gerekir \u2014 bir \u00e7\u00f6z\u00fcc\u00fc arac\u0131n bu kadar zaman kazand\u0131rmas\u0131n\u0131n nedeni de budur.<\/p>\n<p>Hesaplay\u0131c\u0131 \u00f6nce \\( x^2 \\) terimini ortadan kald\u0131rarak \u00e7al\u0131\u015f\u0131r. \\( x = t - \\frac{b}{3a} \\) ikamesi, her \u00fc\u00e7\u00fcnc\u00fc dereceden denklemi 16. y\u00fczy\u0131ldan beri bilinen daha basit bir bi\u00e7im olan <em>basitle\u015ftirilmi\u015f k\u00fcbik denklem<\/em> \\( t^3 + pt + q = 0 \\) haline getirir. Cardano form\u00fcl\u00fc daha sonra, k\u00f6kler hesaplanmadan \u00f6nce bile do\u011falar\u0131n\u0131 s\u00f6yleyen diskriminant benzeri bir \\( \\Delta \\) b\u00fcy\u00fckl\u00fc\u011f\u00fc hesaplar: \\( \\Delta &gt; 0 \\) iken bir ger\u00e7ek ve iki karma\u015f\u0131k k\u00f6k, \\( \\Delta = 0 \\) iken t\u00fcm\u00fc ger\u00e7ek ve \u00e7oklu k\u00f6k, \\( \\Delta &lt; 0 \\) iken \u00fc\u00e7 farkl\u0131 ger\u00e7ek k\u00f6k.<\/p>\n<p>\u00c7\u0131kt\u0131y\u0131 yorumlamak kolayd\u0131r. \u00dc\u00e7 k\u00f6k de say\u0131 ise, \\( y = ax^3 + bx^2 + cx + d \\) grafi\u011fi x eksenini bu noktalarda keser (\u00e7oklu k\u00f6kte eksene te\u011fet olur). \u0130ki alanda \u201cKarma\u015f\u0131k k\u00f6k\u201d yaz\u0131yorsa, grafik x eksenini yaln\u0131zca bir kez, g\u00f6sterilen tek ger\u00e7ek k\u00f6kte keser. Gizli kalan iki k\u00f6k bir <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/karmasik-eslenik\/\">e\u015flenik karma\u015f\u0131k say\u0131 \u00e7iftidir<\/a>; bunlar\u0131 <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/karmasik-sayi-hesaplayici\/\">karma\u015f\u0131k say\u0131 hesaplay\u0131c\u0131s\u0131<\/a> ile daha ayr\u0131nt\u0131l\u0131 inceleyebilirsiniz.<\/p>\n<p>\u00dc\u00e7\u00fcnc\u00fc dereceden denklemler uygulamal\u0131 matemati\u011fin her yerinde kar\u015f\u0131m\u0131za \u00e7\u0131kar: geometride kesi\u015fim noktalar\u0131n\u0131 bulmak, lineer cebirde \u00f6zde\u011ferleri hesaplamak, fizikte hacim problemlerini modellemek ve m\u00fchendislik ile ekonomide kararl\u0131l\u0131k analizleri yapmak i\u00e7in kullan\u0131l\u0131rlar.<\/p>\n<h2>Varsay\u0131mlar, S\u0131n\u0131rlamalar ve \u0130pu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>a katsay\u0131s\u0131 s\u0131f\u0131rdan farkl\u0131 olmal\u0131d\u0131r.<\/strong> \\( a = 0 \\) ise denklem asl\u0131nda ikinci derecedendir (ya da birinci dereceden) \u2014 bu durumda ikinci dereceden denklem \u00e7\u00f6z\u00fcc\u00fcy\u00fc kullan\u0131n.<\/li>\n<li><strong>Karma\u015f\u0131k k\u00f6kler i\u015faretlenir, hesaplanmaz.<\/strong> Hesaplay\u0131c\u0131 ger\u00e7ek k\u00f6kleri say\u0131sal olarak raporlar ve ger\u00e7ek olmayan k\u00f6k \u00e7ifti i\u00e7in \u201cKarma\u015f\u0131k k\u00f6k\u201d g\u00f6sterir. Bu, \u00e7\u0131kt\u0131y\u0131 g\u00fcnl\u00fck kullan\u0131m i\u00e7in sade tutar.<\/li>\n<li><strong>5 ondal\u0131k basama\u011fa yuvarlama.<\/strong> Sonu\u00e7lar yuvarland\u0131\u011f\u0131ndan, \\( \\sqrt[3]{2} \\) gibi bir k\u00f6k 1.25992 olarak g\u00f6r\u00fcn\u00fcr. \u00c7o\u011fu ama\u00e7 i\u00e7in bu hassasiyet fazlas\u0131yla yeterlidir; yuvarlanm\u0131\u015f bir k\u00f6k\u00fc denkleme geri koyarsan\u0131z k\u00fc\u00e7\u00fck farklar g\u00f6r\u00fclebilir.<\/li>\n<li><strong>Say\u0131sal u\u00e7 durumlar.<\/strong> \u00c7ok b\u00fcy\u00fck ya da \u00e7ok k\u00fc\u00e7\u00fck katsay\u0131lar kayan nokta yuvarlama hatalar\u0131na yol a\u00e7abilir; matematiksel olarak tam s\u0131f\u0131r olan bir diskriminant \u00e7ok k\u00fc\u00e7\u00fck pozitif ya da negatif bir say\u0131 olarak hesaplanabilir. Bu durumlarda g\u00f6r\u00fcnt\u00fclenen k\u00f6kler son ondal\u0131k basamaklarda farkl\u0131l\u0131k g\u00f6sterebilir.<\/li>\n<li><strong>Descartes kural\u0131yla kontrol edin.<\/strong> \u00c7\u00f6zmeden \u00f6nce, <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/descartes-isaret-kurali\/\">Descartes i\u015faret kural\u0131 hesaplay\u0131c\u0131s\u0131<\/a> ile ka\u00e7 pozitif ve negatif ger\u00e7ek k\u00f6k oldu\u011funu tahmin edebilir, sonra sonucu \u00e7\u00f6z\u00fcc\u00fcn\u00fcn \u00e7\u0131kt\u0131s\u0131n\u0131 sa\u011flama almak i\u00e7in kullanabilirsiniz. Bunun yan\u0131 s\u0131ra, yaln\u0131zca tek bir say\u0131n\u0131n \\( \\sqrt[3]{n} \\) de\u011ferine ihtiyac\u0131n\u0131z oldu\u011funda <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/kup-kok\/\">k\u00fcpk\u00f6k hesaplay\u0131c\u0131s\u0131<\/a> i\u015finize yarar.<\/li>\n<li><strong>\u00d6nce basit \u00e7arpanlara ay\u0131rmay\u0131 deneyin.<\/strong> Her zaman \\( x = 0 \\) k\u00f6k m\u00fc (yani \\( d = 0 \\) m\u0131) kontrol edin ya da 1, \u22121, 2 veya \u22122 gibi bariz bir tam say\u0131 denklemi sa\u011fl\u0131yor mu diye bak\u0131n \u2014 bir k\u00f6k\u00fc \u00e7arpan olarak ay\u0131rmak, \u00fc\u00e7\u00fcnc\u00fc dereceden denklemi zihinden \u00e7\u00f6zebilece\u011finiz bir ikinci dereceden denkleme indirger.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Cardano y\u00f6ntemiyle herhangi bir \u00fc\u00e7\u00fcnc\u00fc dereceden ax\u00b3 + bx\u00b2 + cx + d = 0 denklemini \u00e7\u00f6zer. D\u00f6rt katsay\u0131y\u0131 girin; hesaplay\u0131c\u0131 ger\u00e7ek k\u00f6kleri bulur, karma\u015f\u0131k k\u00f6kleri i\u015faretler ve \u00e7oklu k\u00f6kleri tespit eder.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[16],"class_list":["post-247","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-cebir"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/247","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=247"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/247\/revisions"}],"predecessor-version":[{"id":2996,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/247\/revisions\/2996"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=247"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=247"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}