Question

The following system of equations can be used to find the roots of the equation
x3 + 72 = 5x2 + 18x.

y = x3 + 72
y = 5x2 + 18x

Graph this system of equations on the graphing calculator.

How many intersection points can you see in the default viewing window?
✔ 1
Adjust the window so you can find all of the points of intersection for the system of equations.

What are the roots of the original polynomial equation? Check all that apply.

–6

0

6

–4

3

8

Answer 1

Rearrange to one polynomial:
x^3 + 72 = 5x^2 + 18x → x^3 - 5x^2 - 18x + 72 = 0.

Factor (use synthetic division or inspection; x = 6 is a root):
Divide by (x − 6) → x^2 + x − 12 = 0 → (x + 4)(x − 3) = 0.

So the roots are x = 6, x = −4, and x = 3.

Correct choices: −4, 3, 6. (The default window may show only 1 intersection — you must expand the window to see all three.)