# How do you write a polynomial function of least degree given the zeros #sqrt6#, #-3+sqrt5#?

##### 1 Answer

Apr 8, 2017

#### Explanation:

Since

And since

To get a polynomial of least degree use just these two factors (and a non-0 constant factor if you wish).

**Bonus**

If we wish the polynomial to have integer or rational coefficients, the the conjugates of the given zeros are also zeros.

That would make the zeros:

The factors in this case would be

When we expand, we get

We could also multiply by any non-0 constant.