JEE PYQ: Quadratic Equation Question 43
Question 43 - 2019 (09 Jan Shift 2)
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:
(1) 3
(2) 2
(3) 4
(4) 5
Show Answer
Answer: (1)
Solution
The roots of $6x^2 - 11x + \alpha = 0$ are rational numbers.
$\therefore$ Discriminant $D$ must be perfect square number.
$D = (-11)^2 - 4 \cdot 6 \cdot \alpha$
$= 121 - 24\alpha$ must be a perfect square
Hence, possible values for $\alpha$ are $\alpha = 3, 4, 5$.
$\therefore$ 3 positive integral values are possible.
BETA
