# Polynomial functions, complex zeros

1. Form a polynomial f(x) with real coefficents having the given degree and zeros

Degree 5; Zeros: 2; -i; -7+i

Enter the polynomial f(x)=a(____) type expression using x as the variable.

2. Find a bound on the real zeros of the polynomial function.

F(x)=x^4+x^3-4x-6

Every real zero of f lies between -____and ____ (its not -2 and 2).

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

F(x)=x^3-8x^2+29x-52

Use the complex zeros to write f in factored form

F(x)=____(reduce fractions and simplify roots)

https://brainmass.com/math/basic-algebra/polynomial-functions-complex-zeros-544351

#### Solution Preview

(please see the attached file for the complete solution)

1. Form a polynomial f(x) with real coefficients having the given degree and zeros

Degree 5; Zeros: 2; -i; -7+i

Enter the polynomial f(x)=a(____) type expression using x as the variable

Solution help:

Note 1: Since the polynomial is of degree 5 than it can be factored into 5 factors of the

form (x -a) where a is a zero

i.e.

(please see the attached file)

Note 2: All complex zeros come as conjugate pairs

i.e. if: (please see the attached file)

.

Based on the above:

(please see the attached file)

and:

(please ...

#### Solution Summary

This solution involves finding a polynomial function based on its zeros and finding all the zeros of a given function.