Question

The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation, $6x^2-11x+\alpha =0$ are rational numbers is :

• A. $5$
• B. $4$
• C. $2$
• D. $3$

Answer 1

The correct option is D $3$

$6x^2-11x+\alpha =0$

If roots are rational numbers, then discriminant should be a perfect square.

$D=121-24\alpha$

So, If $\alpha =1$, $D=97$, which is not a perfect square.

$\alpha =2$, $D=73$, which is not a perfect square.

$\alpha =3$, $D=49$, it is a perfect square.

$\alpha =4$, $D=25$, it is a perfect square.

$\alpha =5$, $D=1$, it is a perfect square.

So, number of possible values of $\alpha$ is $3$.