Roots of a Polynomial

Show that the zeros of f\left(x\right)=x^{3}-3x+1 lie in the intervals \left(-2,\,-1\right), \left(0,\,1\right) and \left(1,\,2\right).  Show that the middle zero lies between \displaystyle\frac{1}{3} and \displaystyle\frac{1}{2}.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 1: Question 1, p. 4)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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