Any sketch of a cubic function will show the curve crossing the axis at least once. If it has exactly one real root then it must have two complex conjugate roots as well. While the real root is easily seen as the intercept, the complex roots are not so obvious. This blog however illustrates a simple technique that enables an estimate to be made on them. Given a scaled sketch, nothing more than a ruler and a sharp pencil is required to obtain the estimate.

blog_15_cubic_roots_with_a_ruler.pdf |