Assertion (A)
The equation $2 x^{2} - 4 x + 3 = 0$ has no real roots.

Reason (R)
The equation $a x^{2} + b x + c = 0, (a \neq 0)$ has no real roots, if $(b^{2} - 4 a c) < 0 .$

(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).

$Reason (R) is true . F rom the equation 2 x^{2} - 4 x + 3 = 0, we have: D = {(- 4)}^{2} - 4 \times 2 \times 3 = 16 - 24 = - 8 < 0 Therefore, the given equation has no real roots . Thus, Assertion (A) is true and Reason (R) is a correct explanation of Assertion (A) .$

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