# Maths - Quartics

What is a quartic?

A 4-th degree polynomial.

What’s the largest number of (real) solutions a quartic can have?

$4$.

What’s the smallest number of (real) solutions a quartic can have?

$0$.

I want to make a quartic with only two roots, $3$ and $4$. How could I do this?

\[(x-3)(x-3)(x-4)(x-4)\]

Visualise the quartic $x^2(x-3)(x+3)$?

PHOTO

When sketching a quatic, what’s the process?

- Add the roots to an axis
- Add the y-intercept