# Thread: finding roots of cubics and quartics

1. ## finding roots of cubics and quartics

How can I find the roots of these equations. I.E, how can I factor the cubic to get a binomial and a quadratic so then I can use the quad. formula for the last two factors?

TYIA

$\displaystyle 10x^3-x^2+5x+4=0$

also

$\displaystyle 3x^4+2x^3+7x^2+8x-20=0$

2. Originally Posted by hello
How can I find the roots of these equations. I.E, how can I factor the cubic to get a binomial and a quadratic so then I can use the quad. formula for the last two factors?

TYIA

$\displaystyle 10x^3-x^2+5x+4=0$

also

$\displaystyle 3x^4+2x^3+7x^2+8x-20=0$
You can use the rational roots theorem to give a list of candidate rational roots which you then check to see if one or more is an actual root.

The rational root theorem says that any rational root of a polynomial equation is the ratio of a factor of the constant terma and the coeficient of the highest order term.

so for the cubic here the list of candidates is:

$\displaystyle \pm 1,\ \pm 2,\ \pm4,\ \pm1/2,\ \pm 1/5,\ \pm 2/5,\ \pm 4/5,\ \pm 1/10$

CB