Question

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

• A. 2
• B. 5
• C. 3
• D. 4

Answer 1

Answer: (C)

3

Answer 2

$6x^2 - 11x + \alpha = 0$ 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 $\alpha = 4 \Rightarrow \; \lambda \notin I$ $\alpha = 5 \Rightarrow \; \lambda \notin I$