If \( \int_{0}^{1}\left(1+\sin ^{4} x\right)\left(a x^{2}+b x+c\rig...

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If \( \int_{0}^{1}\left(1+\sin ^{4} x\right)\left(a x^{2}+b x+c\right) d x=\int_{0}^{2}\left(1+\sin ^{4} x\right)\left(a x^{2}+b x+c\right) d x \) then the quadratic equation \( a x^{2}+b x \)
\( \mathrm{P} \) \( +\mathrm{c}=0 \) has

W.
(a) at least one root in \( (1,2) \)
(b) no root in \( (1,2) \)
(c) two equal roots in \( (1,2) \)
(d) both roots imaginary
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