Question

How do I use a graphing calculator to find the real zeros of `f(x)=x^4+x^3-11x^2-9x+18`?

Answer 1

So, I like to use my TI-nspire graphing calculator (handheld) or the desktop software for graphing. Here is the "nice" image of the graph of your polynomial:

I made the window fit the function so that you could see all four of the x-intercepts, or zeros.

Then, I pressed "control T" and inserted a table:

This confirmed what I could see already, that the graph crosses the x-axis at -3, -2, 1 and 3.

If you wish to algebraically prove that those are the correct zeros, you can do synthetic division with all four numbers...I can't think of how to format this to show you here...nor can I think of how to show you long division unless I write it out with my handwriting. If you wish to see either one, please request it!