Find the Viète formula I know that the Viète formula for the equation $ax^2+bx+c=0$ is:
$$x_1+x_2=-\frac{b}{a}$$
$$x_1x_2=\frac{c}{a}$$
But I didnt know which are the formula for the equation $ax^3+bx^2+cx+d=0$.
Please help me. Thanks.

Soppose that $x_1, x_2, x_3$ is zeros of equation $ax^3+bx^2+cx+d=0$. Now we have
$$ax^3+bx^2+cx+d=a(x-x_1)(x-x_2)(x-x_3)$$
$$=a(x^2-xx_1-xx_2+x_1x_2)(x-x_3)$$
$$=a(x^3-x^2x_1-x^2x_2+xx_1x_2-x^2x_3+xx_1x_3+xx_2x_3-x_1x_2x_3)$$
$$=a(x^3-x^2(x_1+x_2+x_3)+x(x_1x_2+x_1x_3+x_2x_3)-x_1x_2x_3)$$
For the F. Viéte formula we have:
$$x_1+x_2+x_3=-\frac{b}{a}$$
$$x_1x_2+x_1x_3+x_2x_3=\frac{c}{a}$$
$$x_1x_2x_3=-\frac{d}{a}$$
