Let a, b, c be real such that ax^2 + bx + c = 0 and x^2 + x + 1 = 0 have a common root. STATEMENT-1: a = b = c. STATEMENT-2: Two quadratic equations with real coefficients cannot have only one imaginary root common.

JEE Advanced Mathematics question

Let be real such that and have a common root. STATEMENT-1: . STATEMENT-2: Two quadratic equations with real coefficients cannot have only one imaginary root common.

(A)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1Correct
(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: (A)

Solution

**Statement-2:** Non-real roots of a real quadratic occur in conjugate pairs; if (non-real) is common, is also a root of both, so both roots are common. **True.** - **Statement-1:** The roots of are

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Question ID VK-110322