Right so I'll make this to the point. The problem is this:
f(x) = x^4 - 12x^3 + 38x^2 + 116x + 65
I have to find all zeros for the equation. Now, the way we were instructed to solve it was to go on our calculator and put it into the graphing calculator and look at the table
As you can see there is only one zero on the table. What our teacher said to do was notice how there would be more zeros if it switched between a negative to a positive. There has to be a zero between there. However, this is not the case. We learned about diving the products over the quotients, but even so there is only one real zero. I even ran it through a calculator and the only real zero is -1. That would be fine but we need to find nonreal ones.
I used synthetic division with the only zero (-1) and after doing synthetic division you get this: x^3 - 13x^2 + 51x + 65. To find all the zeros you'd just do synthetic division again with another zero, but there is no other zero.
I never learned this in math class. What the hell am I supposed to do if there is only one zero? I can obviously use the zeros calculator to find nonreal numbers. What the calculator says is 7 - 4i and 7 + 4i, but how do I get there??
Thanks in advance to @"StevenNL2000"#2
