Find the values of a and b such that (x+1) and (x-3) are the factors of the polynomial,x³+ax²+5x+b About the author Josephine
Answer: a = -6, b = 5 Step-by-step explanation: [tex] {x}^{3} + a {x}^{2} + 5x + b = (x + 1)(x – 3)(cx + b)[/tex] [tex] {x}^{3} + a {x}^{2} + 5x + b = c {x}^{3} + (d – 2c) {x}^{2} – (3c + 2d)x – 3d[/tex] comparing coefficients c = 1, d = -4 a = d – 2c = -6 b = -(3c+2b) Reply
Answer:
a = -6, b = 5
Step-by-step explanation:
[tex] {x}^{3} + a {x}^{2} + 5x + b = (x + 1)(x – 3)(cx + b)[/tex]
[tex] {x}^{3} + a {x}^{2} + 5x + b = c {x}^{3} + (d – 2c) {x}^{2} – (3c + 2d)x – 3d[/tex]
comparing coefficients
c = 1, d = -4
a = d – 2c = -6
b = -(3c+2b)