Question

Find the nature of the roots of the equation 4x² – 4a²x + a⁴ – b⁴ = 0, b ≠ 0.

Answer 1

4x² – 4a²x + a⁴ – b⁴ = 0

Here a = 4, b = – 4a², c = a⁴ – b⁴

D = b² – 4ас

⇒ (– 4a²)² – 4 × 4 × (a⁴ – b⁴)

⇒ 16a⁴ – 16(a⁴ – b⁴)

= 16a⁴ – 16a⁴ + 16b⁴

= 16b⁴ > 0

D > 0

Hence, roots are real and unequal.