Let a,b,c be non-zero real numbers such that _0^1 (1+ ^8x ) (ax^2+bx+c )dx= _0^2 (1+ ^8x ) (ax^2+bx+c )dx. Then the quadratic equation ax^2+bx+c=0 has

JEE Main Mathematics question

Let be non-zero real numbers such that \int_0^1\left(1+\cos^8x\right)\left(ax^2+bx+c\right)dx=\int_0^2\left(1+\cos^8x\right)\left(ax^2+bx+c\right)dx. Then the quadratic equation has

(A)No root in
(B)At least one root in Correct
(C)A double root in
(D)Two imaginary roots

Answer: (B)

Solution

Subtracting the two sides, . The weight is positive and continuous, so if had no zero in it would have one sign

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Question ID VK-014193