Chapter 5 Polynomials and Polynomial Functions - 5.6 Find Rational Zeroes - 5.6 Exercises - Skill Practice - Page 375: 42

Graph C

Given: $f(x)=x^3-3x^2+2$ The leading coefficients: $\pm 1$ The constant terms: $\pm 1, \pm 2$ The possible rational zeros are: $\pm\frac{1}{1},\pm \frac{2}{1}$ Find the solution of the equation: $x=\frac{-b \pm \sqrt b^2-4ac}{2a}=\frac{-(-2)\pm \sqrt (-2)^2-4.1.(-2)}{2(1)}=\frac{2\pm\sqrt 12}{2}=\frac{2\pm2\sqrt 3}{2}=1\pm\sqrt 3$ So, the other zeros are $1+\sqrt 3$ and $1-\sqrt 3$. The correct answer is C