The equation $a x^{2} + b x + c = 0$ ; $a, b, c \in Q, a \neq 0,$ has rational roots if

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$b^{2} - 4 a c$ is perfect square

$b^{2} - 4 a c$ is the perfect square of a rational number.

$b^{2} - 4 a c \geq 0$

$b^{2} - 4 a c > 0$

answer is D.

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Detailed Solution

The given equation $a x^{2} + b x + c = 0$ ;

Here $a, b, c \in Q, a \neq 0,$

Given that roots are rational,

So, by the condition :

For rational roots, discriminant should be a perfect square of a rational number.

$∴$ $b^{2} - 4 a c$ is the perfect square of a rational number.

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