Are $A = \{2, 3\}$ and $B = \{x : x \text{ is a solution of } x^{2} + 5x + 6 = 0\}$ equal?
AYes, $A = B$
BNo — $B = \{-2, -3\}$, not $\{2, 3\}$
CYes, with one common element
DNo — $B$ is empty
Answer & Solution
Correct answer: B. No — $B = \{-2, -3\}$, not $\{2, 3\}$
Factor: $x^{2} + 5x + 6 = (x + 2)(x + 3) = 0 \Rightarrow x = -2, -3$.
So $B = \{-2, -3\} \ne \{2, 3\} = A$.
Sign error trap: students forget that factoring $x^2 + 5x + 6$ gives negative roots.
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