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Let a , b , c be nonzero real numbers su...

Let `a , b , c` be nonzero real numbers such that `int_0^1(1+cos^8x)(a x^2+b x+c)dx` `=int_0^2(1+cos^8x)(a x^2+b x+c)dx=0` Then show that the equation `a x^2+b x+c=0` will have one root between 0 and 1 and other root between 1 and 2.

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