Suppose the coefficients of the cubic polynomial P(x) = a + bx + cx2 + dx3 satisfy

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Suppose the coefficients of the cubic polynomial P(x) = a + bx + cx2 + dx3 satisfy the Equation a + b/2 + c/3 + d/4 = 0 Show that the equation has a root between 0 and 1. Can you generalize this result for an -degree polynomial?
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