Which of the following are answers to the equation below?
\[
x^2 - 4 = 0, \quad x^2 + 5x + 6 = 0
\]
I. \( x = 2 \)
II. \( x = -2 \)
III. \( x = -3 \)
II. \( x = -2 \)
III. \( x = -3 \)
Show Hint
- I and III
- II and III
- I, II, and III
- I only
- II only
The Correct Option is B
Solution and Explanation
From \( x^2 - 4 = 0 \), we get: \[ x^2 = 4 \Rightarrow x = \pm 2. \] From \( x^2 + 5x + 6 = 0 \), factor the quadratic: \[ (x + 2)(x + 3) = 0 \Rightarrow x = -2 \, \text{or} \, x = -3. \]
Step 2: Conclusion.
Thus, the correct answers are \( x = -2 \) and \( x = -3 \), which corresponds to option (B).
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