Question

The number of integral values of $m$ less than $50$ such that the roots of the quadratic equation $m{x}^2+(2m-1)x+(m-2)=0$ are rational are

• A. $6$
• B. $7$
• C. $13$
• D. $14$

Answer 1

The correct option is A $6$

$D=(4m+1)$
Roots are rational if $D$ is a perfect square
Let $4m+1=K^2$
$\therefore m=\frac{K^2-1}{4}$
$\Rightarrow K=\pm 1,\pm 3,\pm 5,\pm 9,\pm 9......$
$\Rightarrow m=0,2,6,12,20,30,42$ but $m\ne 0$
$\Rightarrow$ Number of integral values of $m$ are $6$.