Question

If x^2 + 3x + 5 is a factor of x^4 + ax^2 + b, what is a + b

Answer 1

Step-by-step explanation:

x^2 - 3x + 2 = (x - 2)(x - 1) x = 1, x = 2 make f(x) zero:

X = 1,

1^4 - a(1)^3 + b = 0

a - b = 1

x = 2,

2^4 - a(2)^3 + b = 0 16 - 8a + b =0 -8a + b = -16

=>

a-b=1

-8a + b = -16 a = 15/7, b = 8/7