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(3) (a) Let p be a polynomial of degree n with n distinct root c1,€2, ...,Ca. Show that 1 1 p(r) F (c)(r – G) i=1 Hint. First show that p'(c;) # 0 for all i = 1, 2,...,n. 1 dr. (b) Use (a) to find / z(r+2)(x– 3)(1 – 1)

(3) (a) Let p be a polynomial of degree n with n distinct root c1,€2, ...,Ca. Show that 1 1 p(r) F (c)(r – G) i=1 Hint. First show that p'(c;) # 0 for all i = 1, 2,...,n. 1 dr. (b) Use (a) to find / z(r+2)(x– 3)(1 – 1)

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.5: Complex Zeros And The Fundamental Theorem Of Algebra
Problem 3E: A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is...
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(3) (a) Let p be a polynomial of degree n with n distinct root c1, c2, ..., Cn. Show that 1. 1 p(x) 7(c)(x – c;)' i=1 Hint. First show that p'(c;) # 0 for all i = 1, 2,...,n. (b) Use (a) to find dr. r(x +2)(x – 3)(r – 1)
Transcribed Image Text:(3) (a) Let p be a polynomial of degree n with n distinct root c1, c2, ..., Cn. Show that 1. 1 p(x) 7(c)(x – c;)' i=1 Hint. First show that p'(c;) # 0 for all i = 1, 2,...,n. (b) Use (a) to find dr. r(x +2)(x – 3)(r – 1)
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