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à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ | ¤é¹ËÒã¹ËÑÇ¢é͹Õé |
#1
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[˹ѧÊ×Í ÊÍǹ.] Polynomial equation posn
˹éÒ $123$
1.¨§ËÒ¾ËعÒÁ $P(x)$ ·Ñé§ËÁ´·Õè·ÓãËé $xP(x-1)=(x-26)P(x)$ 2. ãËé $P(x)$ à»ç¹¾ËعÒÁ·Õè¶Ù¡ËÒôéÇ $x-a,x-b,x-c$ áÅéÇàËÅ×ÍàÈÉ $a,b,c$ µÒÁÅӴѺ ¨§ËÒàÈÉàËÅ×ÍàÁ×èÍ $P(x)$ ËÒôéÇ $(x-a)(x-b)(x-c)$ 3. ¨§ËÒ¤èÒ $a,b$ ·Õè·ÓãËé $x^2+1 | (ax+b)(x^5+1)-(5x+1)$ |
#2
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äÁèÃÙéÇèÒàÍÒÁÒãËé·ÓËÃ×ÍÍÂÒ¡ä´éà©ÅÂàËÁ×͹¡Ñ¹¹Ð¤ÃѺ
ä˹æ¼Á¡çà¢éÒÁÒáÅéÇ 1.ÅͧãªéÇÔ¸Õ»ÃÐÁÒ³¹Õé´Ù http://www.artofproblemsolving.com/F...c.php?t=335804 ¶éÒäÁèÅÐàÍÕ´¾ÍÅͧà»Ô´ÊÍǹàÅèÁÊÁ¡ÒÃàªÔ§¿Ñ§¡ìªÑ¹Ë¹éÒ 355 3. á·¹ $x=i,-i$ à»ç¹ÊÁ¡ÒÃÊͧµÑÇá»Ãá¡éËÒ $a,b,$ ä´éËÃ×Íà»ÅèÒäÁèÃÙé Åͧ´Ù¹Ð ¢éÍ 2 ·èÒ¹Í×è¹ÅСѹ¹Ð¤ÃѺ |
#3
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2. Åͧ¾Ô¨ÒóҾËعÒÁ $P(x)-x$ ´ÙÊÔ¤ÃѺ
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site:mathcenter.net ¤Ó¤é¹ |
#4
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ÍéÒ§ÍÔ§:
¼Á·ÓẺ¹Õé¤ÃѺ $P(x)=(x-a)(x-b)(x-c)Q(x)+mx^2+nx+k$ ä´éàÈÉàËÅ×ͤ×Í $x$ |
#5
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ÍÂèÒ§¹ÕéËÃ×Íà»ÅèÒ¤ÃѺ (¾Í´Õ $P(x)$ äÁèµÃ§¡Ñº¤Ø³ lek 2554)
$Q(x)=P(x)-x$ ·ÓãËéä´éÇèÒ $Q(a)=Q(b)=Q(c)=0$ ¹Ñ蹤×Í $a,b,c$ à»ç¹ÃÒ¡¢Í§ $Q(x)$ ´Ñ§¹Ñé¹ $Q(x)=R(x)(x-a)(x-b)(x-c)$ ©Ð¹Ñé¹ $P(x)=R(x)(x-a)(x-b)(x-c)+x$ ä´éàÈÉà»ç¹ $x$ |
#6
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¡çµÃ§ÍÂÙè¹Ô¤ÃѺ
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----/---~Alice~ ¨§ÃѺÃÙéäÇé ª×èÍáËè§ÊÕÊѹ˹Öè§à´ÕÂÇ·ÕèáÊ´§¼Å ---/---- ~Blue~ ¹Õè¤×Í ÊÕáË觤ÇÒÁËÅѧÍѹ¡ÇéÒ§ãËè¢Í§àÇ纺ÍÃì´¹Õé |
#7
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ÍÕ¡¢éÍ˹Ö觤ÃѺ
¨§ËÒ $P(x)$ ·ÕèÁÕ¡ÓÅѧ¹éÍ·ÕèÊØ´·Õèà»ç¹ä»ä´é «Öè§àÁ×èÍËÒôéÇ $(x-1)^2,(x-2)^3$ áÅéÇàËÅ×ÍàÈÉ $2x,3x$ µÒÁÅӴѺ |
#8
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$P(x)=4x^4-27x^3+66x^2-65x+24$
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#9
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·ÓÂѧä§ËÃͤÃѺ
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#10
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ãªé͹ؾѹ¸ì Êдǡ·ÕèÊØ´áÅéǤÃѺ
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