# Complex Zeros of a Polynomial Function Question

• jcsolis
Yes, your work is correct.In summary, a polynomial of degree 5 with zeros 0, -2i, 2+i can be expressed as f(x)= x^5 - 4x^4 + 9x^3 - 16x^2 + 20x.
jcsolis

## Homework Statement

find a polynomial of degree 5 whose coefficients are that has the zeros: 0, -2i, 2+i

none

## The Attempt at a Solution

I know that the two remaining zeros are: 2i and 2-i

the factors are:

x
x-2i
x+2i
x-2-i
x-2+i

After expand all the factors I fininshed with this answer:

f(x)= x^5 - 4x^4 + 9x^3 - 16x^2 + 20x

can somebody check if my work is OK?

Why don't you check it yourself? That certainly is a "polynomial of degree 5". You can put x= 0, x= -2i, and x= 2+ i into that polynomial and see if it is equal to 0.

Yes, your work appears to be correct. You have correctly identified the remaining zeros and used them to create the factors of the polynomial. Your final answer is also in the correct form for a polynomial of degree 5. Great job!

## 1. What are complex zeros of a polynomial function?

Complex zeros of a polynomial function are the values of the independent variable that make the polynomial function equal to zero. They are complex numbers, which have both a real and imaginary part.

## 2. How do you find the complex zeros of a polynomial function?

To find the complex zeros of a polynomial function, you can use the quadratic formula or factor the polynomial into linear and quadratic terms and solve for the zeros using the zero product property.

## 3. Why are complex zeros important in polynomial functions?

Complex zeros are important in polynomial functions because they help us understand the behavior of the function. They can also give us information about the graph of the function, such as the number of turning points and end behavior.

## 4. Can a polynomial function have only complex zeros?

Yes, a polynomial function can have only complex zeros. This means that the function does not intersect the x-axis at any real values, but rather at complex values. This can happen when the function has an even degree and all of its coefficients are complex.

## 5. How do complex zeros affect the graph of a polynomial function?

The complex zeros of a polynomial function affect the graph by causing it to intersect the x-axis at points that are not real numbers. This can result in a graph that is not symmetrical and has a more complicated shape compared to a polynomial function with only real zeros.

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