Expert: Steve Holleran - 9/7/2008

Question
The question is:

How many real roots does the polynomial 2x^5+8x-7 have?

Thank you very much!

Answer
Hi Dan,

I think what you want here is to use Descartes' rule of signs.

It has to do with the number of sign changes as you go through the polynomial.

The number of positive real roots is the number of sign changes in
P(x) , so here, P(x) = 2x^5 + 8x - 7

There is one sign change (from + 8x to -7), so there is one positive real root.

The number of negative real roots is the number of sign changes in
P(-x), and here

P(-x) = 2(-x)^5 + 8(-x) - 7 = -2x^5 - 8x - 7 = no negative real roots.

So, it appears there is only 1 real root.

To check this, you can graph it on a graphing utility and see how many times it crosses the x-axis.



Hope this helps
Steve