$$ f(x) = ax^3 + (b - ad)x^2 + (c - bd)x - cd $$ where $a = 18, b = 4, c = 20$ and $d = 12$. What value of x satisfies the equation $f(x) = 0$?
$$ f(x)=18x^3- 212x^2-28x-240. $$ i was told to slowly try out all $f(x) = 1/-1, 2/-2 , 3/-3$ until i get 0. I can possibly be doing this if the number gets big like this? it would be too time consuming ! Is there a standard and more effective way in doing this ?
Well, you can try to use this result : http://en.wikipedia.org/wiki/Rational_root_theorem. It can help, because you now have only a finite number of possibilities, to find a rational root. But then, irrational and complex roots remains.
Here, you can try x = 12. Then you can factorize the polynom, to get one of degree 2, which is quite simple to solve.