Are $A = \{2, 3\}$ and $B = \{x : x ext{ is a solution of } x^{2} + …

Question

Are $A = \{2, 3\}$ and $B = \{x : x 	ext{ is a solution of } x^{2} + 5x + 6 = 0\}$ equal?

Accepted Answer

B. No — $B = \{-2, -3\}$, not $\{2, 3\}$

Factor: $x^{2} + 5x + 6 = (x + 2)(x + 3) = 0 \Rightarrow x = -2, -3$.
So $B = \{-2, -3\} 
e \{2, 3\} = A$.
Sign error trap: students forget that factoring $x^2 + 5x + 6$ gives negative roots.

Answer

Yes, $A = B$

Answer

Yes, with one common element

Answer

No — $B$ is empty

Are $A = \{2, 3\}$ and $B = \{x : x \text{ is a solution of } x^{2} + 5x + 6 = 0\}$ equal?