# How do you find the zeroes of #f (x) =5x^4 − 2x^2 − 3#?

##### 1 Answer

This function is an example of a *bi-quadratic* function, which is the polynomial function of the *degree* with no terms of an odd *degree*.

The general polynomial of the *degree* looks like this:

Since no odd *degree* terms are present, general expression for a *bi-quadratic* function is:

Finding the values of an unknown

**Step 1**. Substitute

**Step 2**. The above equation is a regular *quadratic equation* that we know how to solve. Its two solutions are:

(solutions might not be *real* if

**Step 3**. Knowing the value of an unknown

(depending on the coefficients, certain solutions might not be *real*)

I think it would be useful for a student who ask this question to do the math with concrete coefficients given in the problem.

As an illustration, here is a graph of the given function that shows where it takes zero values. It shows that this function has only two real values of

graph{5x^4-2x^2-3 [-3, 3, -4, 4]}