equations
Source: Ukraine 1997 grade 11
July 22, 2009
algebra proposedalgebra
Problem Statement
The equation ax^3\plus{}bx^2\plus{}cx\plus{}d\equal{}0 has three distinct solutions. How many distinct solutions does the following equation have:
4(ax^3\plus{}bx^2\plus{}cx\plus{}d)(3ax\plus{}b)\equal{}(3ax^2\plus{}2bx\plus{}c)^2?