Question

Approximate the real number solution(s) to the polynomial function f(x) = x3 + 4x2 + x - 6

Answer 1

I'm getting 3 real solutions out of it. You are probably going to want to have someone else answer this, because I didn't approximate (and honestly, don't even remember how to approximate), but I will tell you the steps I took and the answers I got.

First, I was going to just dump the whole equation into my ti-83, but as luck would have it my batteries are dead... So I had to crank it out by hand. I used something which I think is called the Rational Root theorem and listed the factors of the coefficient of the highest degree variable (in this case x cubed) and the constant (in this case -6). I then started plugging them into the function to see if I could get a zero, which I did with x=1 (try it yourself, if you plug in 1 instead of x the function returns zero). Now that I know that 1 is a zero, I just used synthetic division to divide it out. The remaining equation I had after I divided the 1 out was x^2 + 5x +6, which I then plugged into the quadratic equation (before kicking myself realizing how obvious the factors are...) and the result was x = -2, and -3. So all my zeros together are x = -3, -2, 1. Honestly though, my first line of attack for a question like this is usually to plug it into a graphing calculator.

Answer 2

Thanks. I was taking a practice quiz and had already finished and actually your answer was right lol.