{"id":293,"date":"2026-10-03T13:15:36","date_gmt":"2026-10-03T12:15:36","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/descartes-isaret-kurali\/"},"modified":"2026-10-03T13:15:36","modified_gmt":"2026-10-03T12:15:36","slug":"descartes-isaret-kurali","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/descartes-isaret-kurali\/","title":{"rendered":"Descartes'in \u0130\u015faret Kural\u0131 Hesaplay\u0131c\u0131"},"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\">Polinomlar\u0131n Pozitif ve Negatif Reel K\u00f6klerini \u0130nceleyin<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"293\" data-favorite-title=\"Descartes&#039;in \u0130\u015faret Kural\u0131\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/descartes-isaret-kurali\/\" data-favorite-excerpt=\"Descartes&#039;in \u0130\u015faret Kural\u0131&#039;n\u0131 kullanarak bir polinomun pozitif, negatif ve reel olmayan k\u00f6klerinin say\u0131s\u0131n\u0131 tahmin edin. Olas\u0131 t\u00fcm k\u00f6k say\u0131lar\u0131n\u0131 g\u00f6rmek i\u00e7in katsay\u0131lar\u0131 kuvvetlerin azalan s\u0131ras\u0131na g\u00f6re girin.\" 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\/descartes-isaret-kurali\/\" method=\"POST\" class=\"calculator\" id=\"calculator-293\" data-post=\"293\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Polinom Katsay\u0131lar\u0131<\/label><input type=\"text\" name=\"polinom_katsaylar\" id=\"field-1\" aria-describedby=\"calc-info-1\" step=\"any\" value=\"1 -6 11 -6\"\/><small id=\"calc-info-1\">Polinomun katsay\u0131lar\u0131n\u0131 kuvvetlerin azalan s\u0131ras\u0131na g\u00f6re, bo\u015flukla ay\u0131rarak girin. \u00d6rne\u011fin: &quot;1 -6 11 -6&quot; ifadesi x\u00b3 - 6x\u00b2 + 11x - 6 polinomunu temsil eder<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"293\">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>Polinomunuz<\/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>S\u0131f\u0131r\u0131n k\u00f6k olarak \u00e7oklu\u011fu<\/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>Pozitif k\u00f6k say\u0131s\u0131<\/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>Negatif k\u00f6k say\u0131s\u0131<\/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 class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>Ger\u00e7ek olmayan k\u00f6klerin en az say\u0131s\u0131<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/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=\"293\" 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>Descartes'in \u0130\u015faret Kural\u0131 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\\[\nP(x) = a_nx^n + a_{n-1}x^{n-1} + \\dots + a_1x + a_0 \\\\[1em]\nV(x) = \\text{P(x) katsay\u0131lar\u0131ndaki i\u015faret de\u011fi\u015fimlerinin say\u0131s\u0131} \\\\[1em]\nN_{\\text{poz}} \\le V(x), \\quad N_{\\text{poz}} \\equiv V(x) \\pmod{2} \\\\[1em]\nN_{\\text{neg}} \\le V(-x), \\quad N_{\\text{neg}} \\equiv V(-x) \\pmod{2}\n\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(P(x)\\) \u2014 polinom, katsay\u0131lar\u0131 kuvvetlerin azalan s\u0131ras\u0131na g\u00f6re yaz\u0131lm\u0131\u015f<\/li>\n<li>\\(V(x)\\) \u2014 \\(P(x)\\)'in ard\u0131\u015f\u0131k s\u0131f\u0131rdan farkl\u0131 katsay\u0131lar\u0131 aras\u0131ndaki i\u015faret de\u011fi\u015fimlerinin say\u0131s\u0131<\/li>\n<li>\\(V(-x)\\) \u2014 \\(P(-x)\\)'teki, yani t\u00fcm tek kuvvetli terimlerin i\u015faretleri ters \u00e7evrilmi\u015f polinomdaki i\u015faret de\u011fi\u015fimlerinin say\u0131s\u0131<\/li>\n<li>\\(N_{\\text{poz}}\\), \\(N_{\\text{neg}}\\) \u2014 pozitif ve negatif reel k\u00f6klerin say\u0131s\u0131, \u00e7okluklar\u0131yla birlikte say\u0131l\u0131r<\/li>\n<\/ul>\n<p>Kurala g\u00f6re pozitif reel k\u00f6klerin say\u0131s\u0131, \\(P(x)\\)'teki i\u015faret de\u011fi\u015fimlerinin say\u0131s\u0131na e\u015fittir ya da bundan \u00e7ift say\u0131da azd\u0131r. Ayn\u0131s\u0131, \\(x\\) yerine \\(-x\\) yaz\u0131ld\u0131\u011f\u0131nda negatif k\u00f6kler i\u00e7in de ge\u00e7erlidir.<\/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>Descartes'in \u0130\u015faret Kural\u0131 \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \\(f(x) = x^3 - 6x^2 + 11x - 6\\) polinomunu alal\u0131m; katsay\u0131lar olarak <code>1 -6 11 -6<\/code> \u015feklinde girilir.<\/p>\n<p><strong>1. Ad\u0131m \u2014 pozitif k\u00f6kler.<\/strong> \\(f(x)\\)'in katsay\u0131lar\u0131n\u0131n i\u015faretleri \u015funlard\u0131r:<\/p>\n<p>\\[ +,\\ -,\\ +,\\ - \\quad \\Rightarrow \\quad 3 \\text{ i\u015faret de\u011fi\u015fimi} \\]<\/p>\n<p>Dolay\u0131s\u0131yla tam olarak 3 ya da tam olarak 1 pozitif reel k\u00f6k vard\u0131r.<\/p>\n<p><strong>2. Ad\u0131m \u2014 negatif k\u00f6kler.<\/strong> \\(-x\\) yerine koyun:<\/p>\n<p>\\[ f(-x) = -x^3 - 6x^2 - 11x - 6 \\]<\/p>\n<p>\u0130\u015faretler \\(-, -, -, -\\) olup 0 i\u015faret de\u011fi\u015fimi verir; b\u00f6ylece negatif reel k\u00f6k yoktur.<\/p>\n<p><strong>Sonu\u00e7:<\/strong> 3 veya 1 pozitif k\u00f6k, 0 negatif k\u00f6k ve en az \\(3 - 3 = 0\\) reel olmayan k\u00f6k. Ger\u00e7ekte \\(f(x) = (x-1)(x-2)(x-3)\\) oldu\u011fundan \u00fc\u00e7 k\u00f6k\u00fcn de (1, 2, 3) pozitiftir.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r<\/h2>\n<ol>\n<li><strong>Polinom Katsay\u0131lar\u0131<\/strong> alan\u0131na, polinomunuzun katsay\u0131lar\u0131n\u0131 kuvvetlerin azalan s\u0131ras\u0131na g\u00f6re, bo\u015fluklarla ay\u0131rarak yaz\u0131n. \u00d6rne\u011fin <code>1 -6 11 -6<\/code> ifadesi \\(x^3 - 6x^2 + 11x - 6\\) polinomunu belirtir.<\/li>\n<li>Bir kuvvet eksikse s\u0131f\u0131r katsay\u0131lar\u0131 da yaz\u0131n: <code>2 0 -5 1<\/code> ifadesi \\(2x^3 - 5x + 1\\) demektir. Ba\u015ftaki ve sondaki s\u0131f\u0131rlar otomatik olarak ele al\u0131n\u0131r.<\/li>\n<li><strong>Hesapla<\/strong> d\u00fc\u011fmesine bas\u0131n.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: hesaplay\u0131c\u0131 polinomunuzu standart bi\u00e7imde g\u00f6sterir; s\u0131f\u0131r\u0131n k\u00f6k olarak \u00e7oklu\u011funu (sabit terim 0 ise), pozitif reel k\u00f6klerin olas\u0131 say\u0131lar\u0131n\u0131, negatif reel k\u00f6klerin olas\u0131 say\u0131lar\u0131n\u0131 ve reel olmayan (karma\u015f\u0131k) k\u00f6klerin en az say\u0131s\u0131n\u0131 verir.<\/li>\n<\/ol>\n<h2>Descartes'in \u0130\u015faret Kural\u0131 size ne s\u00f6yler<\/h2>\n<p>Descartes'in \u0130\u015faret Kural\u0131, 1637'de Ren\u00e9 Descartes taraf\u0131ndan yay\u0131mlanan, bir polinomun ka\u00e7 pozitif ve negatif reel k\u00f6k\u00fc olabilece\u011fini \u2014 denklemi ger\u00e7ekten \u00e7\u00f6meden \u2014 s\u0131n\u0131rlayan h\u0131zl\u0131 bir testtir. Polinomu standart bi\u00e7imde yazars\u0131n\u0131z ve ard\u0131\u015f\u0131k s\u0131f\u0131rdan farkl\u0131 katsay\u0131lar\u0131n ka\u00e7 kez i\u015faret de\u011fi\u015ftirdi\u011fini sayars\u0131n\u0131z. Bu say\u0131n\u0131n kendisi ya da bir \u00e7ift say\u0131 kadar azalt\u0131lm\u0131\u015f h\u00e2li, pozitif k\u00f6klerin kesin say\u0131s\u0131d\u0131r. Ayn\u0131 say\u0131m\u0131 \\(f(-x)\\) \u00fczerinde tekrarlamak negatif k\u00f6kler i\u00e7in olas\u0131l\u0131klar\u0131 verir.<\/p>\n<p>\"\u00c7ift say\u0131 kadar fark\" k\u0131sm\u0131 \u00f6nemlidir. 3 i\u015faret de\u011fi\u015fimi varsa polinomun 3 veya 1 pozitif k\u00f6k\u00fc vard\u0131r \u2014 2 veya 0 oldu\u011fu garanti edilmez; yaln\u0131zca 3 veya 1 m\u00fcmk\u00fcnd\u00fcr. Tam olarak 1 i\u015faret de\u011fi\u015fimi varsa polinomun tam olarak 1 pozitif k\u00f6k\u00fc vard\u0131r ve bu, kural\u0131n en kullan\u0131\u015fl\u0131 \u00f6zel durumlar\u0131ndan biridir.<\/p>\n<p>\u0130ki say\u0131m\u0131 polinomun derecesiyle birle\u015ftirmek, reel olmayan k\u00f6klerin en az say\u0131s\u0131n\u0131 da verir. \\(n\\) dereceli bir polinomun toplam tam olarak \\(n\\) k\u00f6k\u00fc oldu\u011fundan (\u00e7oklu\u011fuyla birlikte say\u0131ld\u0131\u011f\u0131nda, Cebirin Temel Teoremi'ne g\u00f6re) ve reel olmayan k\u00f6kler her zaman e\u015flenik \u00e7iftler h\u00e2linde geldi\u011finden, dereceden reel k\u00f6klerin olas\u0131 en b\u00fcy\u00fck say\u0131lar\u0131n\u0131 \u00e7\u0131kar\u0131rsan\u0131z karma\u015f\u0131k k\u00f6klerin en az say\u0131s\u0131n\u0131 bulursunuz. Bunlar\u0131 incelemek i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/karmasik-kok\/\">Karma\u015f\u0131k K\u00f6k Hesaplay\u0131c\u0131<\/a> ve <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/karmasik-eslenik\/\">Karma\u015f\u0131k E\u015flenik Hesaplay\u0131c\u0131<\/a> sayfalar\u0131na bak\u0131n.<\/p>\n<h2>Sonu\u00e7lar\u0131n yorumlanmas\u0131<\/h2>\n<p>Her sonu\u00e7 sat\u0131r\u0131, kural ile uyumlu t\u00fcm olas\u0131l\u0131klar\u0131 listeler. Pozitif k\u00f6kler i\u00e7in \"3 veya 1\" ifadesi, her iki sonucun da i\u015faret d\u00fczeniyle uyumlu oldu\u011fu anlam\u0131na gelir; ger\u00e7ek say\u0131y\u0131 kesinle\u015ftirmek i\u00e7in ek bilgi (bir grafik, rasyonel k\u00f6k testleri veya say\u0131sal y\u00f6ntemler) gerekir. Tam olarak 0 sonucu kesindir: \\(f(-x)\\)'te i\u015faret de\u011fi\u015fimi yoksa, o polinomun negatif reel k\u00f6k\u00fc yoktur, nokta.<\/p>\n<p>Sabit terim s\u0131f\u0131rsa \\(x = 0\\) bir k\u00f6kt\u00fcr ve hesaplay\u0131c\u0131, sondaki s\u0131f\u0131r katsay\u0131lar\u0131 sayarak \u00e7oklu\u011funu bildirir. Bu durumda kural\u0131, \\(x^k\\) \u00e7arpan\u0131na ayr\u0131ld\u0131ktan sonra kalan polinoma uygulay\u0131n.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlamalar ve ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Katsay\u0131lar reel olmal\u0131d\u0131r.<\/strong> Kural, karma\u015f\u0131k katsay\u0131l\u0131 polinomlara uygulanmaz.<\/li>\n<li><strong>\u0130\u015faret de\u011fi\u015fimleri say\u0131l\u0131rken s\u0131f\u0131r katsay\u0131lar atlan\u0131r.<\/strong> \\(x^3 + 1\\) i\u00e7in i\u015faretler \\(+, +\\)'dir \u2014 \\(f(-x)\\) de kontrol edildi\u011finde tek bir i\u015faret de\u011fi\u015fimi bulunur, dolay\u0131s\u0131yla tam olarak 1 negatif k\u00f6k vard\u0131r.<\/li>\n<li><strong>Kural \u00e7oklu\u011fu sayar.<\/strong> \\(x = 2\\)'de iki katl\u0131 bir k\u00f6k, iki pozitif k\u00f6k olarak say\u0131l\u0131r.<\/li>\n<li><strong>Olas\u0131l\u0131klar\u0131 verir, kesin de\u011ferleri de\u011fil.<\/strong> Kural size k\u00f6klerin ne oldu\u011funu asla s\u00f6ylemez, yaln\u0131zca her i\u015faretten ka\u00e7 tanesinin var olabilece\u011fini s\u00f6yler. Di\u011fer ara\u00e7lar\u0131 uygulamadan \u00f6nce aramay\u0131 daraltmak i\u00e7in kullan\u0131n.<\/li>\n<li><strong>S\u0131f\u0131r k\u00f6kler h\u0131zl\u0131 bir kontrol sa\u011flar:<\/strong> tek dereceli bir polinomun \\(f(x)\\)'te i\u015faret de\u011fi\u015fimi yoksa, en az bir negatif k\u00f6k\u00fc olmak zorundad\u0131r; \u00e7\u00fcnk\u00fc tek dereceli polinomlar\u0131n her zaman en az bir reel k\u00f6k\u00fc vard\u0131r.<\/li>\n<li>Kural, <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/kubik-denklem\/\">K\u00fcbik Denklem Hesaplay\u0131c\u0131<\/a> ve <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/dorduncu-dereceden-denklem\/\">D\u00f6rtl\u00fc (Kuartik) Denklem Hesaplay\u0131c\u0131<\/a> gibi denklem \u00e7\u00f6z\u00fcc\u00fclerle birlikte \u00f6zellikle iyi \u00e7al\u0131\u015f\u0131r ve <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ikinci-derece-denklem-cozucu\/\">\u0130kinci Derece Denklem Hesaplay\u0131c\u0131<\/a> ile bulunan k\u00f6k yap\u0131s\u0131n\u0131 do\u011frulayabilir.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Descartes'in \u0130\u015faret Kural\u0131'n\u0131 kullanarak bir polinomun pozitif, negatif ve reel olmayan k\u00f6klerinin say\u0131s\u0131n\u0131 tahmin edin. Olas\u0131 t\u00fcm k\u00f6k say\u0131lar\u0131n\u0131 g\u00f6rmek i\u00e7in katsay\u0131lar\u0131 kuvvetlerin azalan s\u0131ras\u0131na g\u00f6re girin.<\/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-293","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\/293","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=293"}],"version-history":[{"count":4,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/293\/revisions"}],"predecessor-version":[{"id":2934,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/293\/revisions\/2934"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=293"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=293"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=293"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}