find the roots of this equation 2x^3-3x^2+12x+9=0 ?? show the procedure without using calculator??
Heh. This is a pretty tough one. You have to factor the equation, but I've been having some trouble doing that.
The rational root theorem says that any rational (fractional) root of the equation will be of the form p/q, where p is a factor of 9 (so +/- 1, 3, 9) and q is a factor of 2 (so +/- 1, 2). That gives a bunch of choices to try, but they are the only choices. Use synthetic division to see which root(s) divide in to the original without a remainder.
I have no idea how to do this but see if this will help you. By the looks of it the root looks really ugly. http://www.wolframalpha.com/input/?i=2x^3-3x^2%2B12x%2B9