Question

Finding the real solutions in an equation without graphing. I don't know how to do it without putting it in a graphing calculator which we can not use. x^3-2x^2-5x=-6

Answer 1

\[x ^{3}-2x ^{2}-5x=-6\]

Answer 2

First rewrite your equation to have everything on one side. So it becomes x^3 - 2x^2 - 5X + 6 = 0. Now you'll need to use a little trial and error to find one root. A root is where the graph hits the x axis. So I usually try x = 1 or x = -1 to start with. Sometimes you'll need to try higher numbers. You'll find if you substitute x = 1 into the equation, that leads to a zero so you know one of the roots is at x = 1. Now look up how to do polynomial long division. It's easy. It's almost like regular division. You will divide your equation above by (x - 1). If x = 1 is a root, then x - 1 = 0. That's why you divide by x-1. You'll end up with (x-1)(x^2 - x - 6) being equal to your original equation. If you want to check it, just multiply everything out. Now you can factor the quadratic. So you end up with (x-1)(x+2)(x-3). Therefore there are root at x = 1, -2 and 3.

Answer 3

Thanks .. I needed this for tomorrow.