Question

If one root of the quadratic equation $x^2+qx+2=0$ is double the other, then the value of $q=$

• A. $2$
• B. $3$
• C. $-2$

Answer 1

The correct option is B $3$

Given quadratic equation $x^2+qx+2=0$
Let $\alpha$ be one of the roots
Thus, the second root will be $2\alpha$
Now, for any quadratic equation $a{x}^2+bx+c=0$ having roots as $p,r$
The Sum of Roots: $p+r=-\frac{b}{a}$
And, Product of Roots: $pr=\frac{c}{a}$

Thus, for the given equation, Product of Roots is given as:
$\alpha \times 2\alpha =2\Rightarrow 2{\alpha }^2=2$
$\Rightarrow {\alpha }^2=1\Rightarrow \alpha =\pm 1$
Case $I:\alpha =1$
Sum of Roots $\alpha +2\alpha =-q$
$\Rightarrow q=-3\alpha =-3$
Case $II:\alpha =-1$
Sum of Roots $\alpha +2\alpha =-q$
$\Rightarrow q=-3\alpha =3$