If a, b, c are non-zero real numbers such that

 $\underset{0}{\overset{1}{\int }}(1+{\cos }^8 \mathrm{x})({\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c})\mathrm{dx}=$$\underset{0}{\overset{2}{\int }}(1+{\cos }^8 \mathrm{x})({\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c})\mathrm{dx}=0,$ then the equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ will have

both the roots between 0 and 1

one root between 0 and 1 and other root between 1 and 2

both the roots between 1 and 2

both the roots between (3, $\infty$ )