The equation $ ax^3+bx^2+cx+d=0$ has three distinct solutions. How many distinct solutions does the following equation have: $ 4(ax^3+bx^2+cx+d)(3ax+b)=(3ax^2+2bx+c)^2?$
Source: Ukraine 1997 grade 11
Tags: algebra proposed, algebra
The equation $ ax^3+bx^2+cx+d=0$ has three distinct solutions. How many distinct solutions does the following equation have: $ 4(ax^3+bx^2+cx+d)(3ax+b)=(3ax^2+2bx+c)^2?$