Question

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

9x² + 3kx + 4 = 0

Answer 1

The given equation is 9x² + 3kx + 4 = 0 

∴ D = (3k)² – 4 × 9 × 4

= 9k² – 144 

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

∴ 9k² – 144 > 0 

⇒ 9(k² – 16) > 0 

⇒ (k – 4) (k + 4) > 0 

⇒ k < –4 or k > 4