第一次习题è®&um

第一次习题è®&um

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ֻ 1 Ցษંज़ Exercise 1 a,b,c ൞೘۱҂๝֥ඔđႨ x - a,x - b,x - c Ԣ၂ჭ؟ཛ f ( x ) ֥Ⴥൔ၇Ցູ r,s,t đ൫౰Ⴈ g ( x ) = ( x - a )( x - b )( x - c ) Ԣ f ( x ) ֥ Ⴥൔb ࢳğ ഡ f ( x ) = q ( x ) g ( x ) + r ( x ) đᄵॖഡ r ( x ) = a 2 x 2 + a 1 x + a 0 đ Ⴎ Ⴟ g ( x ) ൞ ೘ Ց ؟ ཛ ൔ đ ܣđ r ( x ) ҂ӑݖؽՑb r ( a ) = f ( a ) = r đ r ( b ) = f ( b ) = s đ r ( c ) = f ( c ) = t b ႮႿ g ( a ) = g ( b ) = g ( c ) = 0 b ܣႵೂ༯ٚӱቆğ 1 a a 2 1 b b 2 1 c c 2 a 0 a 1 a 2 = r s t ಸၞ๙ݖᆃ۱ٚӱቆࢳԛ a 0 ,a 1 2 ֥ᆴđՖط֤֞ r ( x ) b Exercise 2 p,q,r ᆭࡗ֥ܱ༢đ൐֤ x 3 + px 2 + qx + r ֥۴Ӯ֩б ඔਙb ࢳğ ഡ x 3 + px 2 + qx + r ֥೘۱۴ٳљູ x 0 a ,x 0 ,ax 0 đᄵႵ x 3 + px 2 + qx + r = ( x - x 0 a )( x - x 0 )( x - ax 0 ) b ࡼႷൔᅚषđьႵğ p = - ( x 0 a + x 0 + ax 0 ) q = x 2 0 a + x 2 0 + ax 2 0 r = - x 3 0 ႮՎđьႵ ( q p ) 3 = r b Exercise 3 ೂݔ಩ၩ؟ཛൔࠇᆀა؟ཛൔ p ( x ) ޺෍đࠇᆀିФ p ( x ) Ԣđ൫ᆣૼ p ( x ) ҂ॖჿb ᆣૼğ Ⴈّᆣمb ࡌഡ p ( x ) ॖჿđᄵ҂ٞഡ p ( x ) = p 1 ( x ) p 2 ( x ) đఃᇏđ deg p i ( x ) < deg p ( x ) , i = 1 , 2 bՖط p 1 ( x ) ࠻҂ა p ( x ) ޺෍đႻ҂ିФ p ( x ) ᆜԢb઱؛Ć ܣđ p ( x ) ҂ॖჿbᆣиb Exercise 4 ࠢކ R n = { ( a 1 2 ,...,a n ) T | a i R } ܱႿइᆔ֥ࡆمބඔ Ӱ (1) ൞ڎܒӮႵ৘ඔთഈ֥ཌྟॢࡗĤ (2) ൞ڎܒӮگඔთഈ֥ཌྟॢࡗĤ ࢳğ (1) ཁಖđ R n ܱႿइᆔ֥ࡆمބඔӰđܒӮႵ৘ඔთഈ֥ཌྟॢ ႮႿ R n ؓႿൌඔთܒӮཌྟॢ ࡗđطႵ৘ඔთЇݣႿൌඔთđ ၹՎఃؓႿႵ৘ඔთсܒӮཌྟ ॢࡗb ࡗb 1
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(2) R n ܱႿइᆔ֥ࡆمބඔӰđ҂ܒӮگඔთഈ֥ཌྟॢࡗb ཁಖ R
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第一次习题è®&um

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