Question

Let a, b, c be real such that ax² + bx + c = 0 and x² + x + 1= 0 have a common root

Statement–1 : a = b = c

Statement–2 : Two quadratic equations with real coefficients can not have only one imaginary root common.

(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. 

(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1.

(C) Statement – 1 is True, Statement – 2 is False. 

(D) Statement – 1 is False, Statement – 2 is True

Answer 1

Correct option  (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. 

Explanation:

x² + x + 1 = 0 

D = – 3 < 0 

∴ x² + x + 1 = 0 and ax² + bx + c = 0 have both the roots common 

⇒ a = b = c.