Question

What is the root of the polynomial equation x(x-2)(x+3)= 18? Use a graphing calculator and a system of equations.

-3
0
2
3

Answer 1

3

Explanation:

on edge

Answer 2

x = 3

Explanation:

You want the root of the polynomial equation x(x -2)(x +3) = 18.

Graph

A graph of the equation in the form x(x -2)(x +3) -18 = 0 is attached. The solution is the x-intercept. It shows the only real root is x = 3.

System of equations

There are many ways the polynomial can give rise to a system of equations. The basic idea is to write two expressions that are supposed to be equal to each other. The graphing calculator can show the value(s) of x that make them equal.

Dividing both sides of the given polynomial by (x -2)(x +3) gives the equation ...

x = 18/((x -2)(x +3))

This can be graphed as two equations:

y = x

y = 18/((x -2)(x +3))

This is shown in the second attachment. It tells us the root is x=3. (Both sides of the "x=" equation have the value 3 at x=3.)

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Additional comment

Here, you are asked to use a system of equations. A graphing calculator can usually find the solution more easily when the equation is written in the form f(x) = 0. Often x-intercepts are easier to identify than points where graphs cross each other.