The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation, $6 x^2-11 x+ \alpha=0$ are rational numbers is
Select the correct option:
A
4
B
5
C
2
D
3
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
The roots of $6 x^2-11 x+\alpha=0$ are rational numbers.
∴ Discriminant D must be perfect square number.
$$
\begin{aligned}
& D=(-11)^2-4 \cdot 6 \cdot \alpha \\
= & 121-24 \alpha \text { must be a perfect square } \\
\therefore & \alpha=3,4,5
\end{aligned}
$$
$\therefore 3$ positive integral values are possible.
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