Finding the Roots of 4x^3 - 18x^2 + 24x - 10

[andreipanait]

Which method should I use to find the roots of the following polynomial:

. . .4x^3 - 18x^2 + 24x - 10

This is already in derivative form. I'm solving the roots of the derived function in this case. Due to the highest exponent being 3, I can't use the Quadratic Formula, and I can't (or rather don't know how) to simplify it as to be a quadratic.

Thanks

 

[andreipanait]

factor theorem

Oh nvm I read somewhere on the internet that I could use the factor theorem

 

[galactus]

If you look careful, you don't have to use the rational root theorem.

\(\displaystyle \L\\4x^{3}-18x^{2}+24x-10\)

\(\displaystyle \L\\2(2x^{3}-9x^{2}+12x-5)\)

\(\displaystyle \L\\2(2x(x^{2}-2x+1)-5(x^{2}-2x+1))\)

\(\displaystyle \L\\2(2x-5)(x-1)^{2}\)

 

[andreipanait]

:O

thanks for the help