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Question

Assertion (A)
The equation x2 + x + 1 = 0 has both real roots.

Reason (R)
The equation ax2 + bx + c = 0, (a ≠ 0) has both real roots, if (b2 − 4ac) > 0.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Solution

(d) Assertion (A) is false and Reason (R) is true.

Reason (R) is true.For the equation x2 + x + 1 = 0, we have:D = 12 4 × 1 × 1 = 3 < 0This implies that both the roots of the equation are imaginary.Therefore, Assertion(A) is false.Thus, Reason (R) is true and Assertion(A) is false.

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