If p and q are odd integers, then the roots o | vedclass

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(A) The given quadratic equation is $2px^{2} + (2p + q)x + q = 0$.The discriminant $D$ is given by $D = b^{2} - 4ac$.Substituting the coefficients $a

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(A) The given quadratic equation is $2px^{2} + (2p + q)x + q = 0$.The discriminant $D$ is given by $D = b^{2} - 4ac$.Substituting the coefficients $a = 2p$, $b = (2p + q)$, and $c = q$:$D = (2p + q)^{2} - 4(2p)(q)$$D = 4p^{2} + q^{2} + 4pq - 8pq$$D = 4p^{2} + q^{2} - 4pq$$D = (2p - q)^{2}$Since $p$ and $q$ are integers, $D$ is a perfect square of an integer.For a quadratic equation with rational coefficients, if the discriminant is a perfect square, the roots are rational.

If $p$ and $q$ are odd integers, then the roots of the equation $2px^{2} + (2p + q)x + q = 0$ are

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