Precalculus Examples

Identify the Zeros and Their Multiplicities
To find the roots/zeros of the function, set the function equal to and solve.
Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Set equal to and solve for .
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Set the factor equal to .
Add to both sides of the equation.
Set equal to and solve for .
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Set the factor equal to .
Subtract from both sides of the equation.
Solve the equations for . The multiplicity of a root is the number of times the root appears. For example, a factor of would have a root at with multiplicity of .
(Multiplicity of )
(Multiplicity of )
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