Question

If a, b, c be the sides of ∆ABC and equations ax² + bx + c = 0 and 5x² + 12x + 13 = 0 have a common root, then ∠C is –

• A. 60⁰
• B. 90⁰
• C. 120⁰
• D. 45⁰

Answer 1

Answer: (B)

90⁰

Answer 2

For equation

(ii) D = (12)² – 4 . 5 . 13 = – 116 < 0

Hence root of equation (ii) are non-real

Hence both equations have same roots

so a : b : c = 5 : 12 : 13

Let a = 5k, b = 12k, c = 13k

Here c² = a² + b²

⇒ ∠C = 90⁰