Comprehensive type question. Repeated roots: If equation f(x) = 0, where f(x) is a polynomial function, has roots a, a, B,.. or a root is repeated root, then f(x)=0 is equivalent to (x – a) (x – B)...= 0, from whichwe can conclude that f'(x) = 0 or 2(x – a)[(x – B)..]+ (x – a)²[x – B).I'= 0 or (x – a) 2{(x – B) ..·}+ (x - a){(x – B) ...}'|= 0 has root a. Thus, if a root occurs twice in the,equation, then it is common in equations f(x) = 0 and f'(x) = 0. Similarly, if a root occurs thrice in equation, then it is common in the equations f(x)=0, f'(x) = 0, and f"(x) = 0.If a root occurs p times and B root occurs q times in polynomial equation f(x)=0 of degree n(1

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Repeated roots: If equation f(x) = 0, where f(x) is a polynomial function, has roots a, a, 3, or a root is repeated root, then f(x)=0 is equivalent to (x - a) (x - 3)..= 0, from which we can conclude that f'(x) = 0 or 2(x - a)(x - 3).+ (- a)*[(x - B3).. = 0 or (a - a) )2{(x-B)..}+ (- a){(x - 8)...}'=0 has root a. Thus, if a root occurs twice in the, equation, then it is common in equations f(x) = 0 and f'(x) = 0. Similarly, if a root occurs thrice in equation, then it is common in the equations f(x)=0, f'(x) = 0, and f"(x) = 0. If a root occurs p times and 3 root occurs q times in polynomial equation f(x)=0 of degree n(1

Repeated roots: If equation f(x) = 0, where f(x) is a polynomial function, has roots a, a, 3, or a root is repeated root, then f(x)=0 is equivalent to (x - a) (x - 3)..= 0, from which we can conclude that f'(x) = 0 or 2(x - a)(x - 3).+ (- a)*[(x - B3).. = 0 or (a - a) )2{(x-B)..}+ (- a){(x - 8)...}'=0 has root a. Thus, if a root occurs twice in the, equation, then it is common in equations f(x) = 0 and f'(x) = 0. Similarly, if a root occurs thrice in equation, then it is common in the equations f(x)=0, f'(x) = 0, and f"(x) = 0. If a root occurs p times and 3 root occurs q times in polynomial equation f(x)=0 of degree n(1

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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