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
3
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B
1
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C
2
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D
4
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Solution

## The correct option is A 3Given equation is 6x2−11x+α=0 Using discriminant method, x=−b±√D2a If roots are rational numbers, then discriminant should be a perfect square. D=b2−4ac ⇒D=121−24α So, If α=1, D=121−24=97, which is not a perfect square. α=2, D=121−24(2)=73, which is not a perfect square. α=3, D=121−24(3)=49, it is a perfect square. α=4, D=121−24(4)=25, it is a perfect square. α=5, D=121−24(5)=1, it is a perfect square. If we take greater values of α, then D will become negative. So, number of possible values of α is 3.

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