Find the values of a and b such that (x+1) and (x-3) are the factors of the polynomial,x³+ax²+5x+b​

Question

Find the values of a and b such that (x+1) and (x-3) are the factors of the polynomial,x³+ax²+5x+b​

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Josephine 2 months 2021-07-27T23:14:26+00:00 1 Answers 0 views 0

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    2021-07-27T23:15:53+00:00

    Answer:

    a = -6, b = 5

    Step-by-step explanation:

     {x}^{3}  + a {x}^{2}  + 5x + b = (x + 1)(x - 3)(cx + b)

     {x}^{3}  + a {x}^{2}  + 5x + b = c {x}^{3} + (d - 2c) {x}^{2}  - (3c + 2d)x - 3d

    comparing coefficients

    c = 1, d = -4

    a = d – 2c = -6

    b = -(3c+2b)

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