{"id":651,"date":"2026-10-03T15:00:11","date_gmt":"2026-10-03T14:00:11","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/dorduncu-dereceden-denklem\/"},"modified":"2026-10-03T15:00:11","modified_gmt":"2026-10-03T14:00:11","slug":"dorduncu-dereceden-denklem","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/dorduncu-dereceden-denklem\/","title":{"rendered":"D\u00f6rd\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\">D\u00f6rd\u00fcnc\u00fc Dereceden Denklemleri \u00c7\u00f6z\u00fcn<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"651\" data-favorite-title=\"D\u00f6rd\u00fcnc\u00fc Dereceden Denklem\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/dorduncu-dereceden-denklem\/\" data-favorite-excerpt=\"a, b, c, d ve e katsay\u0131lar\u0131n\u0131 girerek herhangi bir d\u00f6rd\u00fcnc\u00fc dereceden ax\u2074 + bx\u00b3 + cx\u00b2 + dx + e = 0 denklemini \u00e7\u00f6z\u00fcn. Hesaplay\u0131c\u0131, Ferrari y\u00f6ntemini kullanarak d\u00f6rt k\u00f6k\u00fcn tamam\u0131n\u0131 \u2014 ger\u00e7el ya da karma\u015f\u0131k \u2014 bulur.\" 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\/dorduncu-dereceden-denklem\/\" method=\"POST\" class=\"calculator\" id=\"calculator-651\" data-post=\"651\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">a<\/label><input type=\"number\" name=\"a\" id=\"field-1\" placeholder=\"1\" step=\"1\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">b<\/label><input type=\"number\" name=\"b\" id=\"field-2\" placeholder=\"-3\" step=\"1\" value=\"-3\"\/><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">c<\/label><input type=\"number\" name=\"c\" id=\"field-3\" placeholder=\"3\" step=\"1\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">d<\/label><input type=\"number\" name=\"d\" id=\"field-4\" placeholder=\"-1\" step=\"1\" value=\"-1\"\/><\/div><div class=\"field\" id=\"input-5\"><label for=\"field-5\">e<\/label><input type=\"number\" name=\"e\" id=\"field-5\" placeholder=\"0\" step=\"1\" value=\"0\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"651\">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 class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>K\u00f6k x\u2084<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/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=\"651\" 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>D\u00f6rd\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^4 + bx^3 + cx^2 + dx + e = 0, \\quad a \\neq 0 \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(a, b, c, d, e\\) \u2014 polinomun ger\u00e7el katsay\u0131lar\u0131<\/li>\n<li>\\(a\\) \u2014 ba\u015fkatsay\u0131 (s\u0131f\u0131r olmamal\u0131d\u0131r, aksi h\u00e2lde denklem d\u00f6rd\u00fcnc\u00fc dereceden olmaz)<\/li>\n<li>\\(x\\) \u2014 \u00e7\u00f6z\u00fclecek bilinmeyen<\/li>\n<\/ul>\n<p>Bu, d\u00f6rd\u00fcnc\u00fc dereceden polinom denkleminin genel bi\u00e7imidir. Analitik \u00e7\u00f6z\u00fcmde Ferrari y\u00f6ntemi kullan\u0131l\u0131r: denklem \u00f6nce \u00e7arpans\u0131z (indirgenmi\u015f) d\u00f6rd\u00fcnc\u00fc derece forma indirgenir (\\(x^3\\) terimi ortadan kalkar), ard\u0131ndan bir \u00e7\u00f6z\u00fcc\u00fc (rezolvent) \u00fc\u00e7\u00fcnc\u00fc derece denklem \u00e7\u00f6z\u00fcl\u00fcr ve d\u00f6rt k\u00f6k, bu \u00fc\u00e7\u00fcnc\u00fc derece denklemin \u00e7\u00f6z\u00fcm\u00fcn\u00fc i\u00e7eren ifadelerin karek\u00f6klerinden elde edilir. Bu hesaplay\u0131c\u0131 t\u00fcm i\u015flemleri otomatik olarak yapar.<\/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>D\u00f6rd\u00fcnc\u00fc Dereceden Denklem \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \\(x^4 - 3x^3 + 3x^2 - x = 0\\) denklemini \u00e7\u00f6zelim; bu, \\(a = 1\\), \\(b = -3\\), \\(c = 3\\), \\(d = -1\\), \\(e = 0\\) varsay\u0131lan de\u011ferlerine kar\u015f\u0131l\u0131k gelir.<\/p>\n<p>\\[ x^4 - 3x^3 + 3x^2 - x = x(x^3 - 3x^2 + 3x - 1) = x(x - 1)^3 = 0 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(x_1 = 0\\) ve \\(x_2 = x_3 = x_4 = 1\\). Denklemin 0'da bir basit k\u00f6k\u00fc ve 1'de bir \u00fc\u00e7 katl\u0131 k\u00f6k\u00fc vard\u0131r \u2014 hesaplay\u0131c\u0131n\u0131n verdi\u011fi de ayn\u0131 d\u00f6rt de\u011ferdir.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>\\(x^4\\) teriminin katsay\u0131s\u0131 olan <strong>a<\/strong> de\u011ferini girin. S\u0131f\u0131rdan farkl\u0131 olmal\u0131d\u0131r.<\/li>\n<li>\\(x^3\\) teriminin katsay\u0131s\u0131 olan <strong>b<\/strong> de\u011ferini girin.<\/li>\n<li>\\(x^2\\) teriminin katsay\u0131s\u0131 olan <strong>c<\/strong> de\u011ferini girin.<\/li>\n<li>\\(x\\) teriminin katsay\u0131s\u0131 olan <strong>d<\/strong> de\u011ferini girin.<\/li>\n<li>Sabit terim olan <strong>e<\/strong> de\u011ferini girin. Denklemin sabit terimi yoksa 0 girin.<\/li>\n<li>\\(x_1\\)'den \\(x_4\\)'e kadar d\u00f6rt k\u00f6k\u00fc okuyun. Karma\u015f\u0131k k\u00f6kler \\(p + qi\\) veya \\(p - qi\\) bi\u00e7iminde g\u00f6r\u00fcn\u00fcr.<\/li>\n<\/ol>\n<p>Eksi i\u015faretli katsay\u0131lar i\u00e7in negatif de\u011ferler girin \u2014 \u00f6rne\u011fin \\(x^4 - 3x^3\\) i\u00e7in a = 1 ve b = \u22123 girin. Denklem i\u00e7eride otomatik olarak normalize edilir; bu nedenle 0.5 gibi kesirli de\u011ferler dahil, s\u0131f\u0131rdan farkl\u0131 her ba\u015fkatsay\u0131 \u00e7al\u0131\u015f\u0131r (0.5 olarak veya ondal\u0131k ad\u0131mlarla girilir).<\/p>\n<h2>D\u00f6rd\u00fcnc\u00fc Dereceden Denklem Nedir?<\/h2>\n<p>D\u00f6rd\u00fcnc\u00fc dereceden denklem, derecesi d\u00f6rt olan bir polinom denklemdir. Cebirin temel teoremine g\u00f6re, kat\u0131l\u0131klar\u0131yla (\u00e7okluklar\u0131yla) birlikte say\u0131ld\u0131\u011f\u0131nda karma\u015f\u0131k d\u00fczlemde her zaman tam olarak d\u00f6rt k\u00f6k\u00fc vard\u0131r. Katsay\u0131lara ba\u011fl\u0131 olarak bu k\u00f6klerin tamam\u0131 ger\u00e7el, tamam\u0131 karma\u015f\u0131k veya ikisinin kar\u0131\u015f\u0131m\u0131 olabilir. Buraya girilen katsay\u0131lar ger\u00e7el oldu\u011fu i\u00e7in, karma\u015f\u0131k k\u00f6kler her zaman <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/karmasik-eslenik\/\">e\u015flenik \u00e7iftler<\/a> h\u00e2linde \\(p \\pm qi\\) olarak gelir.<\/p>\n<p>D\u00f6rd\u00fcnc\u00fc derece, k\u00f6klerin radandallerle (radikal ifadelerle) genel \u00e7\u00f6z\u00fcm\u00fcn\u00fcn bulundu\u011fu en y\u00fcksek derecedir. 16. y\u00fczy\u0131lda ke\u015ffedilen Ferrari y\u00f6ntemi, problemi bir <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/kubik-denklem\/\">\u00fc\u00e7\u00fcnc\u00fc dereceden denkleme<\/a> (rezolvent) indirger ve ard\u0131ndan karek\u00f6klerle tamamlar. Hesaplay\u0131c\u0131n\u0131n yaln\u0131zca say\u0131sal tahminler de\u011fil, kesin cebirsel de\u011ferler verebilmesinin nedeni budur. Bunun bedeli, tam kapal\u0131 bi\u00e7imli ifadenin son derece uzun olmas\u0131d\u0131r; pratikte bu y\u00fczden bu t\u00fcr otomatik ara\u00e7lar kullan\u0131l\u0131r.<\/p>\n<p>Sonu\u00e7lar\u0131 yorumlamak kolayd\u0131r: ger\u00e7el k\u00f6kler, polinom e\u011frisinin x eksenini kesti\u011fi noktalard\u0131r; karma\u015f\u0131k k\u00f6kler ise e\u011frinin o konumlarda eksene de\u011fmedi\u011fini g\u00f6sterir. Tekrarlanan k\u00f6kler (yukar\u0131daki \u00f6rnekteki \u00fc\u00e7 katl\u0131 k\u00f6k gibi), e\u011frinin o noktada eksene te\u011fet oldu\u011funu ifade eder. \u00c7\u00f6zmeden \u00f6nce ka\u00e7 ger\u00e7el k\u00f6k beklenece\u011fine dair h\u0131zl\u0131 bir fikir edinmek isterseniz, <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/descartes-isaret-kurali\/\">Descartes \u0130\u015faret Kural\u0131<\/a> kullan\u0131\u015fl\u0131 bir kontrold\u00fcr.<\/p>\n<p>K\u00f6kler ile katsay\u0131lar aras\u0131ndaki yararl\u0131 ba\u011f\u0131nt\u0131lar (Vieta ba\u011f\u0131nt\u0131lar\u0131) yan\u0131tlar\u0131 do\u011frulaman\u0131z\u0131 sa\u011flar:<\/p>\n<ul>\n<li>\\(x_1 + x_2 + x_3 + x_4 = -b\/a\\)<\/li>\n<li>\\(x_1 x_2 x_3 + x_1 x_2 x_4 + x_1 x_3 x_4 + x_2 x_3 x_4 = -d\/a\\)<\/li>\n<li>\\(x_1 x_2 x_3 x_4 = e\/a\\)<\/li>\n<\/ul>\n<h2>Varsay\u0131mlar, S\u0131n\u0131rlamalar ve \u0130pu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>a katsay\u0131s\u0131 s\u0131f\u0131r olmamal\u0131d\u0131r.<\/strong> a = 0 girerseniz hesaplay\u0131c\u0131 hata bildirir, \u00e7\u00fcnk\u00fc denklem art\u0131k d\u00f6rd\u00fcnc\u00fc dereceden de\u011fildir. \\(a = 0\\) ama \\(b \\neq 0\\) ise asl\u0131nda \u00fc\u00e7\u00fcnc\u00fc dereceden bir denkleminiz vard\u0131r; bunun yerine <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ucuncu-dereceden-denklem\/\">\u00dc\u00e7\u00fcnc\u00fc Dereceden Denklem<\/a> hesaplay\u0131c\u0131s\u0131n\u0131 kullan\u0131n. Hem a hem b s\u0131f\u0131rsa <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ikinci-derece-denklem-cozucu\/\">\u0130kinci Dereceden Denklem<\/a> hesaplay\u0131c\u0131s\u0131n\u0131 kullan\u0131n.<\/li>\n<li><strong>K\u00f6kler<\/strong> \u00fc\u00e7 ondal\u0131k basama\u011fa yuvarlan\u0131r; bu y\u00fczden \\(\\sqrt{2}\\) gibi kesin de\u011ferler 1.414 olarak g\u00f6r\u00fcn\u00fcr. Birbirine \u00e7ok yak\u0131n k\u00f6kler, hafif\u00e7e farkl\u0131 olsalar bile yuvarlama sonras\u0131 ayn\u0131 g\u00f6r\u00fcnebilir.<\/li>\n<li><strong>Say\u0131sal duyarl\u0131k:<\/strong> son derece b\u00fcy\u00fck ya da k\u00fc\u00e7\u00fck katsay\u0131larda ara ad\u0131m olan rezolvent \u00fc\u00e7\u00fcnc\u00fc derece denklem duyarl\u0131k kaybedebilir. Denkleme \u00f6l\u00e7ekleme yapmak (t\u00fcm katsay\u0131lar\u0131 10'un bir kuvvetine b\u00f6lmek) kararl\u0131l\u0131\u011f\u0131 art\u0131r\u0131r.<\/li>\n<li><strong>Karma\u015f\u0131k \u00e7\u0131kt\u0131<\/strong> normaldir: hesaplay\u0131c\u0131 \\(2 + 3i\\) ve \\(2 - 3i\\) gibi \u00e7iftler d\u00f6nd\u00fcr\u00fcyorsa, polinomun o konumlarda ger\u00e7el k\u00f6k\u00fc yoktur. Bu t\u00fcr de\u011ferler hakk\u0131nda daha fazla bilgi i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/karmasik-kok\/\">Karma\u015f\u0131k K\u00f6k<\/a> hesaplay\u0131c\u0131s\u0131na bak\u0131n.<\/li>\n<li><strong>\u00c7okluk say\u0131l\u0131r:<\/strong> her zaman d\u00f6rt k\u00f6k rapor edilir, bu nedenle bir iki katl\u0131 k\u00f6k iki kez g\u00f6r\u00fcn\u00fcr. Yukar\u0131daki \u00f6rnekte \\(x = 1\\), \u00fc\u00e7 katl\u0131 bir k\u00f6k oldu\u011fu i\u00e7in \u00fc\u00e7 kez listelenir.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>a, b, c, d ve e katsay\u0131lar\u0131n\u0131 girerek herhangi bir d\u00f6rd\u00fcnc\u00fc dereceden ax\u2074 + bx\u00b3 + cx\u00b2 + dx + e = 0 denklemini \u00e7\u00f6z\u00fcn. Hesaplay\u0131c\u0131, Ferrari y\u00f6ntemini kullanarak d\u00f6rt k\u00f6k\u00fcn tamam\u0131n\u0131 \u2014 ger\u00e7el ya da karma\u015f\u0131k \u2014 bulur.<\/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-651","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\/651","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=651"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/651\/revisions"}],"predecessor-version":[{"id":2994,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/651\/revisions\/2994"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=651"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=651"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}