Problem

Problem

If a,b,ca, b, c are non-zero real numbers such that ∫01(1+cos⁡6x)(ax2+bx+c)dx=0\int_{0}^{1} (1 + \cos^6 x)(ax^2 + bx + c) dx = 0 , then the equation ax2+bx+c=0ax^2 + bx + c = 0 will have a. one root between 0 and 1 and another between 1 and 2 b. both the roots between 0 and 1 c. both the roots between 1 and 2 d. None of the above

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