Suppose $P(x) $ is a polynomial satisfying $ P(0) = 1, P(1) = 2, P(2) = 5, P(3) = 10, P(4) = 17$

Question

Suppose $P(x) $ is a polynomial satisfying $ P(0) = 1, P(1) = 2, P(2) = 5, P(3) = 10, P(4) = 17$. Is $P(5)$ uniquely determined by these conditions? Justify your answer. Hint: Consider the polynomial $ P(x) - x^2 - 1$.

Accepted Answer

Not uniquely determined; $P_t(5)=26+120t$ for any real $t$.

Polynomials, Cubic Equations and Partial Fractions - Forming Polynomials from Roots and Factors

Polynomials, Cubic Equations and Partial Fractions - Forming Polynomials from Roots and Factors

Solution:

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