Question

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

• A. 2
• B. 5
• C. 3
• D. 4

Answer 1

Answer: (C)

$6x^2-11x+\alpha =0$
given roots are rational
$\Rightarrow D$ must be perfect square
$\Rightarrow 121-24\alpha ={\lambda }^2$
$\Rightarrow$ maximum value of $\Rightarrow$ is 5
$\alpha =1\Rightarrow \lambda \notin I$
$\alpha =2\Rightarrow \lambda \notin I$
$\alpha =3\Rightarrow \lambda \notin I\Rightarrow 3$ integral values
$\alpha =4\Rightarrow \lambda \notin I$
$\alpha =5\Rightarrow \lambda \notin I$