AMC 12 2019b 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 $\{a,b,c\}=\{r,s\}$.)

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