Question

If p(x) =x^3 - px^2 + qx - 9 has a factor of x^2 + 3, find 2p - q​

Answer 1

Answer:

2p - q = 3

Step-by-step explanation:

If p(x) =x^3 - px^2 + qx - 9 has a factor of x^2 + 3, find 2p - q​

p(x) = x³ - px² + qx - 9

g(x) = x² + 3

Let say

q(x) = (x + a)

g(x) * q(x) = (x² + 3)(x + a)

= x³ + ax² + 3x + 3a

Equating with

x³ - px² + qx - 9

a = - p

q = 3

3a = - 9

=> a = -3

-3 = -p => p = 3

2p - q = 2 * 3 - 3 = 3