Let a be a repeated root of a quadratic equation f (x) = 0and A(x), B(x), C(x) be polynomials of degrees 3, 4, and 5,respectively, then show thatB(x) C(x)A(x)A(α) B(α)A'(a) B'(a)() denotes the derivatives.C(a) is divisible by f(x), where primeC'(a)

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Answered: Let a be a repeated root of a quadratic…

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 A(x) B(x) C(x) A(α) B(α) C(a) is divisible by f(x), where prime