The number of real solution(s) of the equation \( x^2 + 3x + 2 = \min \left( |x - 3|, |x + 2| \right) \) is:
Show Hint
- \( 1 \)
- \( 3 \)
- \( 0 \)
- \( 2 \)
The Correct Option is A
Solution and Explanation
We are tasked with solving the equation \( x^2 + 3x + 2 = \min \left( |x - 3|, |x + 2| \right) \). First, we analyze the behavior of the minimum function, which requires us to consider the cases for \( |x - 3| \) and \( |x + 2| \). After checking these cases, we find that the equation has exactly one real solution.
Final Answer: \( 1 \).
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