# Identify the Zeros and Their Multiplicities f(x)=2x^4-9x^2+3 To find the roots/zeros, set equal to and solve.
Substitute into the equation. This will make the quadratic formula easy to use.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Multiply by .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Multiply by .
Change the to .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Multiply by .
Change the to .
The final answer is the combination of both solutions.
Substitute the real value of back into the solved equation.
Solve the first equation for .
Solve the equation for .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Solve the second equation for .
Solve the equation for .
Take the 1th root of each side of the equation to set up the solution for
Remove the perfect root factor under the radical to solve for .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Evaluate as .
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
The solution to is .
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 )
(Multiplicity of )
(Multiplicity of )
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