can anyone show the step how u solve this cubic equation?
1) x^3 - 8.5x²+8x+17.5=0

2)x^3-(2/3)x²-0.11x+0.03=0

Question

can anyone show the step how u solve this cubic equation?
1) x^3 - 8.5x²+8x+17.5=0

2)x^3-(2/3)x²-0.11x+0.03=0

turingtest · Answer

not very pretty...
I would start by getting rid of the decimals and fractions.

turingtest · Answer

Then you can use the rational root theorem and/or Descartes rule of signs to give you an idea for the first solution.
Once you find one you can divide synthetically and get a quadratic.

turingtest · Answer

any progress on that?

turingtest · Answer

Look, if you want the slightly more blunt route just start plugging in numbers like$$0,\pm1,\pm2,\pm3...$$and who know? you may get lucky and find a root. Then you can divide synthetically to get a quadratic, which can be solved more directly.

dumbcow · Answer

Another way is to just graph the function and use the "calc zero" function on your graphing calculator. Then use synthetic division to verify the zeroes.

asnaseer · Answer

or you can use the method described here to find the zeros of any cubic equation: http://www.sosmath.com/algebra/factor/fac11/fac11.html

anonymous · Answer

I will make my progress in learning the rational root theorem and/or Descartes rule of signs first : )