## ROOTS OF EQUATIONS

At the end of this section, students should be able to:

1. test for the existence of a root of $$f(x)=0$$ where f is continuous using the Intermediate Value Theorem;
2. use interval bisection to find an approximation for a root in a given interval;
3. use linear interpolation to find an approximation for a root in a given interval;
4. explain, in geometrical terms, the working of the Newton-Raphson method;
5. use the Newton-Raphson method to find successive approximations to the roots of $$f(x)=0$$, where $$f$$ is differentiable;
6. use a given iteration to determine a root of an equation to a specified degree of accuracy.