Finite Math Examples

Find the Roots (Zeros) f(x)=3x^3-12x^2+3x
Step 1
Set equal to .
Step 2
Solve for .
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Step 2.1
Factor out of .
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Step 2.1.1
Factor out of .
Step 2.1.2
Factor out of .
Step 2.1.3
Factor out of .
Step 2.1.4
Factor out of .
Step 2.1.5
Factor out of .
Step 2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.3
Set equal to .
Step 2.4
Set equal to and solve for .
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Step 2.4.1
Set equal to .
Step 2.4.2
Solve for .
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Step 2.4.2.1
Use the quadratic formula to find the solutions.
Step 2.4.2.2
Substitute the values , , and into the quadratic formula and solve for .
Step 2.4.2.3
Simplify.
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Step 2.4.2.3.1
Simplify the numerator.
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Step 2.4.2.3.1.1
Raise to the power of .
Step 2.4.2.3.1.2
Multiply .
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Step 2.4.2.3.1.2.1
Multiply by .
Step 2.4.2.3.1.2.2
Multiply by .
Step 2.4.2.3.1.3
Subtract from .
Step 2.4.2.3.1.4
Rewrite as .
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Step 2.4.2.3.1.4.1
Factor out of .
Step 2.4.2.3.1.4.2
Rewrite as .
Step 2.4.2.3.1.5
Pull terms out from under the radical.
Step 2.4.2.3.2
Multiply by .
Step 2.4.2.3.3
Simplify .
Step 2.4.2.4
The final answer is the combination of both solutions.
Step 2.5
The final solution is all the values that make true.
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Step 4