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