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# Polynomial functions, complex zeros

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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.

Note 2: All complex zeros come as conjugate pairs
i.e. if: (please see the attached file)
.
Based on the above: