Solutions to problem set: Dr. Cruzan Web: Polynomial Functions - GCF
1. f(x) = 5x4 + 10x 3 - 75x 2
Note: zero is a double root
(see note at the bottom of
the page)
2. f(x) = - 3x5 - 12x 4 - 12x 3
Zero is a triple
root here and
quadruple in #3.
3. f(x) = - 4x6 - 16x 4
4. f(x) = 4x4 + 12x 3 - 112x 2
There is no x-axis crossing
at an imaginary root. It
cannot be graphed on the
x-y plane.
5. f(x) = 7x4 - 42x3 + 63x 2
6. f(x) = 2x5 - 26x3 + 72x
A note on roots: At a single
root, the graph of a function
crosses right through the x-axis.
At a double root it just touches
the axis, and at a triple root
it passed through but the
curvature of the function
changes between concave-up
and concave-down.
© J. Cruzan 2013
Solutions to Web Problems: Polynomial zeros by GCF
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