Let a be a repeated root of a quadratic equation f(x) = 0 and A(x), B(x), C(x) be polynomials of degrees 3, 4, and 5, respectively, then show that A(x) B(x) C(x) A(α) B(α) C(a) is divisible by f(x), where prime
Let a be a repeated root of a quadratic equation f(x) = 0 and A(x), B(x), C(x) be polynomials of degrees 3, 4, and 5, respectively, then show that A(x) B(x) C(x) A(α) B(α) C(a) is divisible by f(x), where prime
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
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![Let a be a repeated root of a quadratic equation f (x) = 0
and A(x), B(x), C(x) be polynomials of degrees 3, 4, and 5,
respectively, then show that
B(x) C(x)
A(x)
A(α) B(α)
A'(a) B'(a)
() denotes the derivatives.
C(a) is divisible by f(x), where prime
C'(a)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0814db3-9aaa-4a26-8c95-9c991cc96947%2F3184b140-0efb-4f4f-bdd2-63f6caa0e23f%2Fthzlw6s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let a be a repeated root of a quadratic equation f (x) = 0
and A(x), B(x), C(x) be polynomials of degrees 3, 4, and 5,
respectively, then show that
B(x) C(x)
A(x)
A(α) B(α)
A'(a) B'(a)
() denotes the derivatives.
C(a) is divisible by f(x), where prime
C'(a)
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