# Polynomials : Zeros and Complex Roots

Find the polynomial f(x) of degree three that has zeroes at 1, 2, and

4 such that f(0) = -16.

a. f (x) = x3 − 7x2 +14x −16

b . f (x) = 2x3 −14x 2 + 28x −16

c . f (x) = 2x3 −14x 2 +14x −16

d . f (x) = 2x3 + 7x2 +14x +16

Find the third degree polynomial whose graph is shown in the figure.

a. f (x) = x3 −x 2 −2x + 2

b . 2

2

1

4

f (x) = 1 x3 − x 2 −x +

c . 2 2

4

1

4

f (x) = 1 x3 − x 2 + x +

d . 2

2

1

2

f (x) = 1 x3 + x 2 −x +

The figure shows the graph of the polynomial function y = f(x). For

which of the values k = 0, 1, 2, or 3 will the equation f(x) = k have

complex roots?

a. 0

b . 1

c . 2

d . 3

https://brainmass.com/math/basic-algebra/polynomials-zeros-and-complex-roots-121326

#### Solution Summary

Polynomials, zeros and complex roots are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.