Question

If x − 4 is a factor of x³ + kx² + 2x − 8, then the value of k is ______.

पर्याय

• −8

• 8

• 4

• −4

Answer 1

If x − 4 is a factor of x³ + kx² + 2x − 8, then the value of k is −4.

Explanation:

Let x − 4 = 0

x = 4

Let f(x) = x³ + kx² + 2x − 8

∵ x − 4 is a factor of f(x).

∴ f(4) = 0

⇒ 4³ + k(4)² + 2(4) − 8 = 0

⇒ 64 + 16k + 8 − 8 = 0

⇒ 64 + 16k = 0

⇒ k = `(-64)/16`

⇒ k = −4