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
(a2−b)x2−2ax+1=0
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B
(a2−b)x2+2ax+1=0
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C
(a2+b)x2−2ax+1=0
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D
(a2+b)x2+2ax+1=0
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Solution
The correct option is A(a2−b)x2−2ax+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,1a−√b Sum of the roots =2aa2−b and product of the roots =1a2−b Hence, the quadratic equation is x2−(2aa2−b)x+1a2−b=0⇒(a2−b)x2−2ax+1=0