If $p + \sqrt{q} \forall p, q \in Z$ is one of the roots of the quadratic equation, then it's other root will be.

p - \sqrt{q}

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- p - \sqrt{q}

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- p + \sqrt{q}

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Solution

The correct option is A $p - \sqrt{q}$
Given: $p + \sqrt{q} \forall p, q \in Z$ is one of the roots of a quadratic equation.
Now, $p + \sqrt{q}$ is an irrational number whose conjugate will be $p - \sqrt{q}$ .
We know, if one of the roots of a quadratic equation with rational coefficients is an irrational number, then it's other root will be it's irrational conjugate.
$\Rightarrow p - \sqrt{q}$ will be the other root of the equation.

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