Question

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

(A)  60° 

(B)  90° 

(C)  120° 

(D)  45°

Answer 1

Correct option (B) 90°

Since 5x² + 12x + 13 = 0 has imaginary roots as D = 144 − 4 x 5 x 13 < 0.

So, both roots of ax² + bx + c = 0 and 5x² + 12x + 13 = 0 will be common.

Hence, a/5 = a/12 = c/13

⇒ a² + b² = c² ⇒ ∠C =  90°