# mathematics

How can one solve polynomial of the form ax^3+bx+c equal zero e.g x^3-27x-27 equal zero

I don't understand the approach u used.make it more clearer by using signs that are understandable.don't use the dollar sign ($) ### Re: mathematics Introduce two variables$u$and$v$linked by the condition$u + v = x$, a straightforward substitution transfroms the initial equation to the following$u^{3}+v^{3}+(3uv + b)(u+v)+ c =0$Impose the additional condition$3uv + b = 0$to deduce the system$u^3 + v^3 = - b $and$u^3 v^3 = -\frac{b^3}{27}$that is equivalent to the fact that the$u^3$and$v^3$are roots of the quadratic equation$z^2 +c z - \frac{b^3}{27} = 0\$.

The method is due to Scipione del Ferro and Tartaglia, published by Gerolamo Cardano in 1545.