Show that the largest positive root of the equaion x^3-3x^2-2=0 lies between 3 and 4.
How do I solve the question? I have no formula to use except trial and error method to find the first root, and then solve the quadratic equation. So how can i tell where the largest positive root of the equation lies?
I think it has something to do with f(3) and f(4), f being the cubic equation's expression, but I just cannot think out the exact procedure.
I have to use a sequence of linear interpolations to estimate this root correct to 2 decimal places later in the same question, so if I am allowed find out the root by trial and error and the quadratic equation it doesn't make any sense to have the second question.
I am really