Question

If the equation (a² + b²) x² – 2 (ac + bd)x + (c² + d²) = 0 has equal roots, then which one of the following is correct ?

(a) ab = cd 

(b) ad = bc 

(c) a² + c² = b² + d² 

(d) ac = bd

Answer 1

(b)  bc = ad.

Equal roots ⇒ Discriminant = 0 

⇒ 4(ac + bd)² – 4(a² + b²) (c² + d²) = 0

⇒ –[b²c² + a²d² – 2acbd] = 0 

⇒ (bc – ad)² = 0 ⇒ bc = ad.