Question

If the roots of equation x² − 6x + k = 0 are real and distinct, then value of k is ______.

Options

• > −9

• > −6

• < 6

• < 9

Answer 1

If the roots of equation x² − 6x + k = 0 are real and distinct, then value of k is < 9.

Explanation:

Given,

Roots of equation x² − 6x + k = 0 are real and distinct.

∴ D > 0

⇒ b² − 4ac > 0

⇒ (−6)² − 4 × 1 × k > 0

⇒ 36 − 4k > 0

⇒ 4k < 36

⇒ k < `36/4`

⇒ k < 9.