Question

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.

• A. $-p-\sqrt{q}$
• B. $-p+\sqrt{q}$
• C. $p-\sqrt{q}$

Answer 1

The correct option is C $p-\sqrt{q}$

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.