Consider the polynomial p(x)=x⁴-3x²-4.how many x-intercepts does the graph of the equation y=x⁴-3x²-4 have? what are the x-intercepts?

The equation has two x-intercepts. They are and .

Step-by-step explanation:

A x-intercept are the values of x when .

The number of x-intercepts is the number of solutions. The x-intercepts are the solutions.

So let's solve the equation:

We have the following equation:

.

The first step to solve this problem is using

We replace in the equation 1, find the values of y, and then we replace in equation 2) to find the values of x.

To solve the equations, it is important to know how we find the roots of a second order polynomial.

Given a second order polynomial expressed by the following equation:

This polynomial has roots such that , given by the following formulas:

In this problem, we have

So

So:

The values of y are

We also have that:

So

And

There is no real solution for this. So our only solutions are and .

So, the equation has two x-intercepts. They are and .

y=mx+b

step-by-step explanation:

m slope, b y-intercept