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$$ f(x) = ax^3 + (b - ad)x^2 + (c - bd)x - cd $$ 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 ?

DanZimm
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Kerry
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1 Answers1

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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.

waffle
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  • alright i'll check it out ! 12 works like a magic, i got 0 straight. i think i will faint from trying all the possibility from 1/-1 till i get 12 ! how did you get 12 may i ask ? – Kerry Apr 05 '15 at 09:35
  • Well, you just have to plot the function to see what is going on. Here, there is a "trivial" integer solution, but it is not always the case... – waffle Apr 05 '15 at 09:57