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​

Answer 1

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)