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Question

If a,b,c are distinct rational numbers, then the roots of the quadratic equation (a+b2c)x2+(b+c2a)x+(c+a2b)=0 are

A
rational and distinct
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B
rational and equal
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C
irrational
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D
imaginary
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Solution

The correct option is A rational and distinct
(a+b2c)x2+(b+c2a)x+(c+a2b)=0
Sum of coefficients =0
Since, the sum of coefficients is zero, so the given quadratic equation has one root to be 1.

Let another root be α.
Product of roots =c+a2ba+b2c
1×α=a+c2ba+b2c
α=a+c2ba+b2c
Roots are rational and distinct.

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