P(x)=3x^3+2x^2-4?

Question

find the zeros of this polynomial function

Answer 1

Are you sure it's the good polynomial function ?
Because there is no rationnal zero...

Answer 2

Hi,
I'll give you the answers and make a few comments.
x1= 0.917439
x2 = -0.792053 -0.908831i
x3 = -0.792053 + 0.908831i

If we try to apply the elementary methods, here are the results (you may have already tried these.)
1) Descartes rule of signs. We find that there is one positive real root (one sign change) and two or zero negative roots (two sign changes in f(-x).
2) The rational zero therem tells us that the possible real, rational roots are:
+-1/3, +-2/3, +4/3
But if we do synthetic division, we find that none of these roots work. So, that about ends our elementary methods.
If we graph the function on a graphing calculator, we find that the only real root is slightly less than 1.0. To get an accurate answer, we can use the "zero" function on the TI-83 plus or TI-84 or we can use the polynomial function on the TI-89 or Casio cfx-9850 series.
If you have one of these calculators, I strongly recomment that you use it unless you are required to show your work.
There are some interative methods and some other methods such as Cardan's method which you can look up if you must show your work. If you must show an analytic method, and you can't get any help, perhaps you could post your question here and state that you must show an analytic method.
Hope this helps some.

FE