# What is the quadratic polynomial function in standard form with zeros 3, 1, 2, and -3?

Jun 20, 2015

It's a quartic (order 4), not a quadratic (order 2), but the simplest example is:

$\left(x - 3\right) \left(x + 3\right) \left(x - 1\right) \left(x - 2\right)$

$= \left({x}^{2} - 9\right) \left({x}^{2} - 3 x + 2\right)$

$= {x}^{4} - 3 {x}^{3} - 7 {x}^{2} + 27 x - 18$

#### Explanation:

To have exactly $4$ distinct zeros, it must have $4$ distinct linear factors, and hence be of the form given.