Question

If the roots of quadratic equation 4x² − 5x + k = 0 are real and equal, then value of k is ______.

Options

• `5/4`

• `25/16`

• `−5/4`

• `−25/16`

Answer 1

If the roots of quadratic equation 4x² − 5x + k = 0 are real and equal, then value of k is `25/16`.

Explanation:

Given that,

Roots of quadratic equation 4x² − 5x + k = 0 are real and equal

On comparing with ax² + bx + c = 0,

We get, a = 4, b = −5 and c = k

For real and equal roots,

⇒ b² − 4ac = 0

⇒ (−5)² − 4(4)(k) = 0

⇒ 16k = 25

⇒ k = `25/16`