Question

If 2x + 1 is a factor of 3 − kx − 2x², then the value of k is ______.

Options

• 5

• −5

• 3

• −3

Answer 1

If 2x + 1 is a factor of 3 − kx − 2x², then the value of k is −5.

Explanation:

Let 2x + 1 = 0

x = `-1/2`

Let f(x) = 3 − kx − 2x²

∵ 2x + 1 is a factor of f(x).

∴ `f(-1/2)` = 0

⇒ `3 - k(-1/2) - 2(-1/2)^2` = 0

⇒ `3 + k/2 - 2(1/4)` = 0

⇒ `3 + k/2 - 1/2` = 0

⇒ `(6 + k - 1)/2` = 0

⇒ 5 + k = 0

⇒ k = −5