• Can you find a cubic equation \(ax^3+bx+c=0\) where (at least) one of the roots of the corresponding quadratic \(ax^2+bx+c=0\) is also a root of the cubic?

Can you sketch what a solution to this problem might look like? What are the important features on this sketch?

How can we use algebra to express the condition that the cubic and quadratic share a root?