ISI2020-MMA: 22

Question

Let $m$ and $n$ be nonzero integers. Define

                             $\text{A}_{m, n}= \left \{ x \in \mathbb{R}:n^{2} x^{3}+ 2020x^{2}+mx = 0\right \}$.

Then the number of pairs $(m, n)$ for which $\text{A}_{m, n}$ has exactly two points is

• A. $0$

• B. $10$

• C. $16$

• D. $\infty$