2019 AMC 12B Problem 21

How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of coefficients? (For clarification: If the polynomial is ax^2+bx+c,a\neq 0, and the roots are r and s, then the requirement is that \{a,b,c\}=\{r,s\}.)

\textbf{(A) } 3 \qquad\textbf{(B) } 4 \qquad\textbf{(C) } 5 \qquad\textbf{(D) } 6 \qquad\textbf{(E) } \text{infinitely many}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.