Question

Find the values of k for which the given quadratic equation has real and distinct roots:

x² – kx + 9 = 0

Answer 1

The given equation is x² – kx + 9 = 0

∴ D = (–k)² – 4 × 1 × 9

= k² – 36

The given equation has real and distinct roots if D > 0.

∴ k² – 36 > 0

⇒ (k – 6) (k + 6) > 0

⇒ k < –6 or k > 6