If _0^1(1+ ^4x)(ax^2+bx+c) ,dx= _0^2(1+ ^4x)(ax^2+bx+c) ,dx then the quadratic equation ax^2+bx+c=0 has

JEE Advanced Mathematics question

If \displaystyle\int_0^1(1+\sin^4x)(ax^2+bx+c)\,dx=\int_0^2(1+\sin^4x)(ax^2+bx+c)\,dx then the quadratic equation has

Answer: (A)

Subtracting, where (not identically zero, being a quadratic).

Suppose had no root in . Then, being continuous, would keep one sign on , and since the integrand would be of one sign and not identically

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Question ID VK-109572