Answer
a. See explanations.
b. $x\approx1.324717957$, see graph.
c. $x\approx1.324717957$
Work Step by Step
a. Evaluate the function at the two values: $f(-1)=(-1)^3-(-1)-1=-1\lt0$ and $f(2)=(2)^3-2-1=5\gt0$. Based on the Intermediate Value Theorem, there must be a value $c$ in $(-1,2)$ such that $f(c)=0$
b. We can find the real solution graphically and identify the zero at $x\approx1.324717957$; see graph.
c. Using a calculator with enough precision, we can evaluate the exact answer as $x\approx1.324717957$ which is exactly the same as the answer in part (b).