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Create a polynomial function that meets the following conditions. Explain how you created your
polynomial.
4. Degree 3, 2 positive real zeros, 1 negative real zero, 0 complex zeros.
Polynomial:
Solution
Polynomial may be : f(x) = -x^3 + x^2 + x - 1 Reasoning : the number of positive roots of the
polynomial is either equal to the number of sign differences between consecutive nonzero
coefficients. so here has two sign change(the sequence of pairs of successive signs is -+, ++, +-).
So it has 2 positive roots. for negative root we change the signs of the coefficients of the terms
with odd exponents, i.e., apply Descartes' rule of signs to the polynomial f(-x), to obtain a
second polynomial f(-x) = x^3 + x^2 - x - 1 it has 1 sign change so f(-x) has one positive root so
f(x) has 1 negative root.

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