Question

If one zero of the polynomial (3x² + 8x + k) is the reciprocal of the other, then value of k is ______.

Options

• 3

• –3

• `1/3`

• `-1/3`

Answer 1

If one zero of the polynomial (3x² + 8x + k) is the reciprocal of the other, then value of k is 3.

Explanation:

Let the zeroes be α and `1/α`.

Product of zeroes = `α * 1/α`

= `"Constant"/("Coefficient of"  x^2)`

⇒ `1 = k/3`

⇒ k = 3