3

Part of 2002 India IMO Training Camp

Problems(1)

Quadratics of the form ax^2+2bx+c

Source: India tst 2002 p3

X=\{2^m3^n|0 \le m, \ n \le 9 \}

. How many quadratics are there of the form

ax^2+2bx+c

, with equal roots, and such that

a,b,c

are distinct elements of

X

quadraticsalgebra proposedalgebra