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Question

The number of all possible positive integral values of α for which the roots of the quadratic equation, 6x211x+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 3
Given equation is 6x211x+α=0
Using discriminant method,
x=b±D2a
If roots are rational numbers, then discriminant should be a perfect square.
D=b24ac
D=12124α
So, If α=1, D=12124=97, which is not a perfect square.
α=2, D=12124(2)=73, which is not a perfect square.
α=3, D=12124(3)=49, it is a perfect square.
α=4, D=12124(4)=25, it is a perfect square.
α=5, D=12124(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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