Find the complex zeros of the following polynomial function. Write f in factored form.

Answered question

2021-10-18

Find the complex zeros of the following polynomial function. Write f in factored form.

f(x)=x38

Answer & Explanation

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-26Added 2605 answers

Given f(x)=x38

Set x38 equal to 0

Solve for x.

Add 8 to each component of the equation.

x3=8

Subtract 8 from both sides of the equation.

x38=0

Factor the left side of the equation

(x2)(x2+2x+4)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x2=0

x2+2x+4=0

Set x2 equal to 0 and solve for x.

x=2

Set x2+2x+4 equal to 0 and solve for x.

x=1+i3,1i3

The final solution is all the values that make (x2)(x2+2x+4)=0 true

Answer: x=2,1+i3,1i3

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