If X is one of the zero of the equation then

a*0^3+ b*0^2+c*0+d=0

(X=0)

Gives d=0

So our final equation is

ax^3+bx^2+cx=0

Take X common and transpose it

X(ax^2+bx+c)=0

ax^2+bx+c=0

Now sum of the roots will be equal to -b/a

And product of root will be c/a