2. For any real numbers $m$, $n$, $p$, it is required:
(1) to write the corresponding quadratic equation;
(2) to make the equation have $n^{2}-4 m p$ as the discriminant.

Among the following answers:
$$
\begin{array}{l}
m x^{2}+n x+p=0, \\
p x^{2}+n x+m=0, \\
x^{2}+n x+m p=0, \\
\frac{1}{a} x^{2}+n x+a m p=0(a \neq 0),
\end{array}
$$

The equation(s) that fully meet the requirements ( ).
(A) exactly 1
(B) exactly 2
(C) exactly 3
(D) all 4
2.B.

When $m=0$, equation (1) is not a quadratic equation; when $p=0$, equation (2) is not a quadratic equation. Equations (3) and (4) are quadratic equations, and both have $n^{2}-4 m p$ as their discriminant.

Explanation: (1) For a quadratic equation in one variable $a x^{2}+b x+c=0$ to be a quadratic equation, the condition $a \neq 0$ must be satisfied;
(2) A quadratic equation $a x^{2}+b x+c=0(a \neq 0)$ corresponds to a unique discriminant $\Delta=b^{2}-4 a c$, but conversely, a quadratic equation in one variable with the discriminant $\Delta=b^{2}-4 a c$ is not unique.