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Question

If a and b are rational numbers and b is not a perfect square, then the quadratic equation with rational coefficients whose one root is 1a+b, is

A
(a2b)x22ax+1=0
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B
(a2b)x2+2ax+1=0
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C
(a2+b)x22ax+1=0
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D
(a2+b)x2+2ax+1=0
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Solution

The correct option is A (a2b)x22ax+1=0
We know that, for a quadratic equation with rational coefficients, irrational roots always occur in conjugate pairs.
So, the roots of the equation are 1a+b,1ab
Sum of the roots =2aa2b
and product of the roots =1a2b
Hence, the quadratic equation is
x2(2aa2b)x+1a2b=0(a2b)x22ax+1=0

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