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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. $\text{Reason}\left(\text{R}\right)\text{is true}\text{.}\phantom{\rule{0ex}{0ex}}\text{For the equation}{x}^{2}+x+1=0,\text{we have:}\phantom{\rule{0ex}{0ex}}D={1}^{2}-4×1×1=-3<0\phantom{\rule{0ex}{0ex}}\mathrm{This}\mathrm{implies}\mathrm{that}\mathrm{b}\text{oth the roots of the equation are imaginary}\text{.}\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},\text{Assertion}\left(\text{A}\right)\text{is false}\text{.}\phantom{\rule{0ex}{0ex}}\text{Thus, Reason}\left(\text{R}\right)\text{is true and Assertion}\left(\text{A}\right)\text{is false}\text{.}\phantom{\rule{0ex}{0ex}}$

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