Question

the following system of equations can be used to find the roots of the equation
\\(x^3 + 72 = 5x^2 + 18x\\).

\\(y = x^3 + 72\\)
\\(y = 5x^2 + 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

Explanation:

Rearrange the polynomial equation into standard form

$$ x^3 - 5x^2 - 18x + 72 = 0 $$

Factor the polynomial by grouping

$$
LATEXBLOCK0
$$

Solve for the roots

$$ x = 3, \quad x = 6, \quad x = -4 $$

Answer:

• -6
• 0
• 6 (Correct answer)
• -4 (Correct answer)
• 3 (Correct answer)
• 8