Food for thought

# How not to solve a cubic... Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Suggestion

• 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?