{"id":10988,"date":"2026-03-26T21:24:49","date_gmt":"2026-03-26T21:24:49","guid":{"rendered":"https:\/\/lereveil224.info\/?post_type=cours&#038;p=10988"},"modified":"2026-03-26T21:28:59","modified_gmt":"2026-03-26T21:28:59","slug":"polynomes-et-fractions-rationnelles","status":"publish","type":"cours","link":"https:\/\/lereveil224.info\/index.php\/cours\/polynomes-et-fractions-rationnelles\/","title":{"rendered":"Polyn\u00f4mes et fractions rationnelles"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>1. Polyn\u00f4mes du second degr\u00e9<\/strong><br><strong>1.1 Forme canonique<\/strong><\/h2>\n\n\n\n<p><strong>a) Cas g\u00e9n\u00e9ral :<\/strong><br>On admet que, pour tout polyn\u00f4me <strong>P<\/strong> du second degr\u00e9, il existe des nombres r\u00e9els <strong>a, \u03b1, \u03b2 avec a \u2260 0<\/strong> tels que, pour tout nombre r\u00e9el x : <strong>P(x) = a(x + \u03b1)\u00b2 + \u03b2<\/strong><br>Cette \u00e9criture de <strong>P(x)<\/strong> est appel\u00e9e forme canonique.<\/p>\n\n\n\n<p><strong>Retenir :<\/strong><br>Pour trouver la forme canonique de <\/p>\n\n\n\n<p><strong>P(x) = ax\u00b2 + bx + c avec a \u2260 0<\/strong><br>&#8211; On met le nombre <strong>a<\/strong> en facteur :<br>\u00a0 <strong>P(x) = a(x\u00b2 + (b\/a)x + c\/a)<\/strong><br>&#8211; On consid\u00e8re que <strong>x\u00b2 + (b\/a)x<\/strong> est le d\u00e9but du d\u00e9veloppement de <strong>(x + b\/2a)\u00b2<\/strong><br>&#8211; On cherche le nombre <strong>\u03b2<\/strong> qu\u2019il faut ajouter pour obtenir <strong>x\u00b2 + (b\/a)x + c\/a<\/strong><\/p>\n\n\n\n<p><strong>Formule g\u00e9n\u00e9rale \u00e0 retenir :<\/strong><br><strong>P(x) = a[(x + b\/2a)\u00b2 &#8211; \u0394 \/ 4a\u00b2]<\/strong><br>avec <strong>\u0394 = b\u00b2 &#8211; 4ac<\/strong><\/p>\n\n\n\n<p><strong>Exemples :<\/strong><br>a) P(x) = x\u00b2 &#8211; 2x + 5<br><strong>P(x) = (x &#8211; 1)\u00b2 + 4<\/strong><\/p>\n\n\n\n<p>b) P(x) = 4x\u00b2 &#8211; 12x &#8211; 7<br><strong>P(x) = 4[(x &#8211; 3\/2)\u00b2 &#8211; 4]<\/strong><br>c) P(x) = -2x\u00b2 &#8211; 5x + 3<br><strong>P(x) = -2[(x + 5\/4)\u00b2 &#8211; 49\/16]<\/strong><br><br><br><br><br><br><\/p>\n","protected":false},"featured_media":0,"template":"","classes":[64,63],"class_list":["post-10988","cours","type-cours","status-publish","hentry","classe-11e-se","classe-11e-sm"],"acf":[],"_links":{"self":[{"href":"https:\/\/lereveil224.info\/index.php\/wp-json\/wp\/v2\/cours\/10988","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lereveil224.info\/index.php\/wp-json\/wp\/v2\/cours"}],"about":[{"href":"https:\/\/lereveil224.info\/index.php\/wp-json\/wp\/v2\/types\/cours"}],"wp:attachment":[{"href":"https:\/\/lereveil224.info\/index.php\/wp-json\/wp\/v2\/media?parent=10988"}],"wp:term":[{"taxonomy":"classe","embeddable":true,"href":"https:\/\/lereveil224.info\/index.php\/wp-json\/wp\/v2\/classes?post=10988"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}