Let m and n be non zero integers. Define $A_{m,n} = \{ x \in R : n^2x^3+2020x^2+mx=0 \}$ Then the number of pairs (m,n) for which $A_{m,n}$ has exactly two points is
(A) 0
(B) 10
(C) 16
(D) $\infty$
My approach is one of the root is x=0 and the quadratic eqn $n^2x^2+2020x+m=0$ must have equal roots.
Condition we get is $n^2m=(101)^2(2)^2(5)^2$. We can choose n^2 4+3C2+1 ways So total no of (m,n) should be 16. Please verify if the solution is correct