Question:
The number of real solution(s) of the equation \( x^2 + 3x + 2 = \min \left( |x - 3|, |x + 2| \right) \) is:
The number of real solution(s) of the equation \( x^2 + 3x + 2 = \min \left( |x - 3|, |x + 2| \right) \) is:
Show Hint
When solving equations involving the minimum of absolute values, break the problem into cases based on the behavior of the absolute values and solve each case separately.
Updated On: Mar 24, 2025
- \( 1 \)
- \( 3 \)
- \( 0 \)
- \( 2 \)
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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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