# Find the Equation Given the Roots 4 , 5i , -5i , ,
Roots are the points where the graph intercepts with the x-axis .
at the roots
The root at was found by solving for when and .
The factor is
The root at was found by solving for when and .
The factor is
The root at was found by solving for when and .
The factor is
Combine all the factors into a single equation.
Multiply all the factors to simplify the equation .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify each term.
Multiply by .
Move to the left of .
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
Simplify each term.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Move to the left of .
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply .
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Multiply by .
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply .
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Multiply by .
Combine the opposite terms in .
Subtract from .
Reorder the factors in the terms and .