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
Expand using the FOIL Method.
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Step 2.1.1
Apply the distributive property.
Step 2.1.2
Apply the distributive property.
Step 2.1.3
Apply the distributive property.
Step 2.2
Simplify terms.
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Step 2.2.1
Combine the opposite terms in .
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Step 2.2.1.1
Reorder the factors in the terms and .
Step 2.2.1.2
Subtract from .
Step 2.2.1.3
Add and .
Step 2.2.2
Simplify each term.
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Step 2.2.2.1
Multiply by .
Step 2.2.2.2
Multiply by .
Step 2.3
Expand using the FOIL Method.
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Step 2.3.1
Apply the distributive property.
Step 2.3.2
Apply the distributive property.
Step 2.3.3
Apply the distributive property.
Step 2.4
Simplify each term.
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Step 2.4.1
Multiply by by adding the exponents.
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Step 2.4.1.1
Multiply by .
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Step 2.4.1.1.1
Raise to the power of .
Step 2.4.1.1.2
Use the power rule to combine exponents.
Step 2.4.1.2
Add and .
Step 2.4.2
Move to the left of .
Step 2.4.3
Multiply by .
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