The equation ax3+bx2+cx+d=0 has three distinct solutions. How many distinct solutions does the following equation have: 4(ax3+bx2+cx+d)(3ax+b)=(3ax2+2bx+c)2?
Source: Ukraine 1997 grade 11
Tags: algebra proposed, algebra
The equation ax3+bx2+cx+d=0 has three distinct solutions. How many distinct solutions does the following equation have: 4(ax3+bx2+cx+d)(3ax+b)=(3ax2+2bx+c)2?