SOLUTION: how do you sketch the graph of a polynomial function that has 3 real zeros, and two imaginary zeros. Like how would you graph this polynomial function 3x^5-4x^4+2x^3-x^2-x-7. It ha

Question 993883: how do you sketch the graph of a polynomial function that has 3 real zeros, and two imaginary zeros. Like how would you graph this polynomial function 3x^5-4x^4+2x^3-x^2-x-7. It has 3 real zeros and 2 imaginary,but I don't know how to graph that.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have to find the roots.
the graph will cross or touch the x-axis at the real roots.
the graph will not cross or touch the x-axis at the imaginary roots.
if the root has an even multiplicity, the graph will touch the x-axis but not cross it.
if the root has an odd multiplicity,the graph will cross the x-axis.
in between the real roots, you just have to test selected points in order to be able to sketch the graph.

check this reference out as it explains how to sketch a graph and it also discusses even roots and odd roots.

the graph of your equation looks like this:

since it only crosses the x-axis once, it has only 1 real root.
the other 4 must be complex.
fyi - complex roots always come in pairs.
you can have 2 or 4, but you can't have 3.

here's a good reference that should help you understand better.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/

lots of good stuff in there.

check out tutorials 38 and 39.

they apply to your question.

basically you are looking for the real roots.

there are all kinds of tests to determine what they are.

once you found those, if the number of roots is not equal to the degree of the equation, then the other roots must be complex.

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