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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15RE
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