The roots of a quadratic equation $a x^{2} + b x + c = 0$ are given by $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , provided $b^{2} - 4 a c \geq 0$ .

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For the quadratic equation ax2+bx+c=0,a,b and c are rational numbers and D=b2−4ac is a non-zero perfect square. The roots of the equation are

The correct option is B Rational and unequalFor ax2+bx+c=0,a,b,c are rational numbers and D=b2−4ac is a non-zero perfect square. ⇒√D>0 ∴x=−b±√D2a has rational and unequal values. Hence, the correct answer is option (2).

For the quadratic equation $a x^{2} + b x + c = 0, a, b$ and $c$ are rational numbers and $D = b^{2} - 4 a c$ is a non-zero perfect square. The roots of the equation are

The correct option is B Rational and unequal
For $a x^{2} + b x + c = 0, a, b, c$ are rational numbers and $D = b^{2} - 4 a c$ is a non-zero perfect square.
$\Rightarrow \sqrt{D} > 0$
$∴ x = \frac{- b \pm \sqrt{D}}{2 a}$ has rational and unequal values.
Hence, the correct answer is option (2).