Precalculus · Problem 3.3.34

Polynomial Functions — Stitz & Zeager

Mathematics — Precalculus · finding-real-zeros-polynomials

Problem

Find the real zeros of f(x)=x3−112x2−772x+172f(x) = x^3 - \dfrac{1}{12}x^2 - \dfrac{7}{72}x + \dfrac{1}{72} by first finding a polynomial q(x)q(x) with integer coefficients such that q(x)=N⋅f(x)q(x) = N \cdot f(x) for some integer NN. (Recall that the Rational Zeros Theorem required the polynomial in question to have integer coefficients.) Show that ff and qq have the same real zeros.

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