The polynomial P(x) = 2x6 + 6x3 + 2x3 - 3x2 + 8x + 1 has two real roots. Determine

Question:

The polynomial P(x) = 2x6 + 6x3 + 2x3 - 3x2 + 8x + 1 has two real roots. Determine integers α and b so that one root is in the interval [α, α + 1] and the other is in the interval [b, b + 1]?

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