Question

if 2 is a root of the equation $p^2{x}^2-5qx-6q=0(p,q\in R)$ then the roots of the equation $x^2+px+q=0$ are

• A. Irrational
• B. Rational and different
• C. Complex conjugate
• D. Rational and equal

Answer 1

The correct option is D

Rational and equal

2 is a root of the equation $p^2{x}^2-5qx-6q=0$
Substituting 2 in the equation, we get
$4p^2-10q-6q=0$
$\Rightarrow 4(p^2-4q)=0$
Or $p^2-4q=0$
The discriminant of the equation $x^2+px+q$ is $p^2-4q=0$
So the roots of the equation are equal and rational