1
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Question

# The number of all possible positive integral values of α for which the roots of the quadratic equation, 6x2−11x+α=0 are rational numbers is :

A
2
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B
3
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C
4
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D
5
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Solution

## The correct option is B 36x2−11x+α=0 If roots are rational numbers, then discriminant should be a perfect square. D=121−24α So, If α=1, D=97, which is not a perfect square. α=2, D=73, which is not a perfect square. α=3, D=49, it is a perfect square. α=4, D=25, it is a perfect square. α=5, D=1, it is a perfect square. So, number of possible values of α is 3.

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