Question

One factor of x³ – kx² + 11x – 6 is x – 1. The value of k is ______.

Options

• – 6

• 12

• 6

• –12

Answer 1

One factor of x³ – kx² + 11x – 6 is x – 1. The value of k is 6.

Explanation:

Let f(x) = x³ – kx² + 11x – 6

Since x – 1 is a factor of f(x)

∴ f(1) = 0

`\implies` 1³ – k · 1² + 11 – 6 = 0

`\implies` 1 – k + 11 – 6 = 0

`\implies` 6 – k = 0

`\implies` k = 6