question_answer

Let a, b, c be non-zero real number such that\[\int_{0}^{1}{(1+{{\cos }^{8}}x)\,\,(a{{x}^{2}}+bx+c)\,\,dx}\]\[=\int_{0}^{2}{(1+{{\cos }^{8}}x)\,\,(a{{x}^{2}}+bx+c)\,\,dx}\]. Then the quadratic equation \[a{{x}^{2}}+bx+c=0\]has

A)  no root in (0, 2)

B)  at least one root in (1, 2)

C)  a double root (0, 2)

D)  All of these

E)  None of these