For a quadratic equation ax^2 + bx + c = 0,if | vedclass

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(B) For a quadratic equation $ax^2 + bx + c = 0$ with rational coefficients $a, b, c \in \mathbb{Q}$,the roots are given by the quadratic formula: $x

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$D$ is a perfect square of a rational number and $a, b, c \in \mathbb{Q}$

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(B) For a quadratic equation $ax^2 + bx + c = 0$ with rational coefficients $a, b, c \in \mathbb{Q}$,the roots are given by the quadratic formula: $x = \frac{-b \pm \sqrt{D}}{2a}$,where $D = b^2 - 4ac$ is the discriminant.$1$. If $D > 0$ and $D$ is a perfect square of a rational number,then $\sqrt{D}$ is rational,making the roots rational and distinct.$2$. If $D = 0$,the roots are real and equal.$3$. If $D Therefore,for the roots to be distinct and rational,$D$ must be greater than $0$ and a perfect square of a rational number,provided $a, b, c$ are rational.

For a quadratic equation $ax^2 + bx + c = 0$,if $\ldots \ldots \ldots \ldots$ then the roots are distinct and rational.

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