Find the solutions to 2x⁴-24x²+40=0 and the x-intercepts of the graph of y=2x⁴-24x²+40.

The solutions and the x-intercepts of the polynomial are:

Step-by-step explanation:

Given a function f a solution or a root of f is a value at which .

An x-intercept is a point on the graph where y is zero.

To find the solutions of the polynomial and the x-intercepts you need to:

First, we need to factor the polynomial expression

Factor the common term

We can treat as a quadratic function with respect to

Let . We can rewrite in terms of as follows:

We need to solve the quadratic equation

for this we can use the Quadratic Equation Formula:

For a quadratic equation of the form the solutions are

the solutions to the quadratic equation are:

Therefore,

Recall that so

Using the Zero factor Theorem: If ab = 0, then either a = 0 or b = 0, or both a and b are 0.

roots are ;

roots are ;

The solutions and the x-intercepts are:

Because all roots are real roots the x-intercepts and the solutions are equal.

step-by-step explanation:

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0