question_answer

Let a, b, c be non-zero real numbers such that \[\int_{0}^{1}{(1+{{\cos }^{8}}x)\,\,(a{{x}^{2}}+bx+c)\,\,dx}=\]\[\int_{0}^{2}{(1+co{{s}^{8}}\,\,x)\,\,(a{{x}^{2}}+bx+c)\,\,dx}\] 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 in (0, 2)

D)  two imaginary roots

E)  None of these