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Polynomials : Zeros and Complex Roots

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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

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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.

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