Examples

Find the Equation with Real Coefficients
, ,
Step 1
Since the roots of an equation are the points where the solution is , set each root as a factor of the equation that equals .
Step 2
Simplify.
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Step 2.1
Simplify by multiplying through.
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Step 2.1.1
Apply the distributive property.
Step 2.1.2
Simplify the expression.
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Step 2.1.2.1
Multiply by .
Step 2.1.2.2
Multiply by .
Step 2.2
Expand using the FOIL Method.
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Step 2.2.1
Apply the distributive property.
Step 2.2.2
Apply the distributive property.
Step 2.2.3
Apply the distributive property.
Step 2.3
Simplify and combine like terms.
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Step 2.3.1
Simplify each term.
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Step 2.3.1.1
Multiply by by adding the exponents.
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Step 2.3.1.1.1
Multiply by .
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Step 2.3.1.1.1.1
Raise to the power of .
Step 2.3.1.1.1.2
Use the power rule to combine exponents.
Step 2.3.1.1.2
Add and .
Step 2.3.1.2
Move to the left of .
Step 2.3.1.3
Rewrite as .
Step 2.3.1.4
Multiply by .
Step 2.3.1.5
Move to the left of .
Step 2.3.1.6
Rewrite as .
Step 2.3.2
Add and .
Step 2.3.3
Add and .
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