(3) (a) Let p be a polynomial of degree n with n distinct root c1, c2, ..., Cn. Show that1.1p(x) 7(c)(x – c;)'i=1Hint. First show that p'(c;) # 0 for all i = 1, 2,...,n.(b) Use (a) to finddr.r(x +2)(x – 3)(r – 1)

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Answered: (3) (a) Let p be a polynomial of degree…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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)