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# Polynomial Functions and Intermediate Value Theorem

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1. Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
F(x)=x^5-x^4+7x^3-8x^2-16x+13; [1.3,1.7]
Find value of f (1.3) ____ (simplify)
Find value of f (1.7) ______ (simplify)

2. Information is given about the polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
Degree 3; Zeros: 4,4-i

3. Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; zeros: 9, -i, -8+i
F(x)=a_______

4. Find the complex zeros of the polynomial function. Write f in factored form.
F(x)=3x^4-19x^3+33x^2+141x-50
F(x)=____.

https://brainmass.com/math/basic-algebra/polynomial-functions-intermediate-value-theorem-544489

#### Solution Preview

1. Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
F(x)=x5-x4+7x3-8x2-16x+13; [1.3,1.7]
Find value of f (1.3)= -5.08417 ____ (simplify)
Find value of f (1.7) ___2.91747___ (simplify)
Since f(1.3)<0 and f(1.7)>0, by IVT, there exists a number c which lies ...

#### Solution Summary

The solution gives detailed steps on solving a series of mathmatical problems: first using intermediate value theorem to show the existance of zeros, then finding zeros (both real and complex) for specific polynomials. Finally, a procedure of factoring polynomial is explained.

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