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Question

# Assertion (A) The equation $2{x}^{2}-4x+3=0$ has no real roots. Reason (R) The equation $a{x}^{2}+bx+c=0,\left(a\ne 0\right)$ has no real roots, if $\left({b}^{2}-4ac\right)<0.$ (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

## (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). $\mathrm{Reason}\left(\text{R}\right)\text{is true}\text{.}\phantom{\rule{0ex}{0ex}}\mathrm{F}\text{rom the equation 2}{x}^{2}-4x+3=0,\text{we have:}\phantom{\rule{0ex}{0ex}}D={\left(-4\right)}^{2}-4×2×3=16-24=-8<0\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},\text{the given equation has no real roots}\text{.}\phantom{\rule{0ex}{0ex}}\text{Thus, Assertion}\left(\text{A}\right)\text{is true and Reason}\left(\text{R}\right)\text{is a correct explanation of Assertion}\left(\text{A}\right).\phantom{\rule{0ex}{0ex}}$

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