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.

Answer 1

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

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