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If |ax^2 + bx+c|<=1 for all x is [0, 1]...

If `|ax^2 + bx+c|<=1` for all x is `[0, 1]`,then

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Let a, b, c be non-zero real numbers such that ; int_0^1 (1 + cos^8 x)(ax^2 + bx + c)dx = int_0^2 (1+cos^8 x)(ax^2 + bx +c)dx then the quadratic equation ax^2 + bx + c = 0 has -