Question

The number of real solution(s) of the equation \( x^2 + 3x + 2 = \min \left( |x - 3|, |x + 2| \right) \) is:

• A. \( 1 \)
• B. \( 3 \)
• C. \( 0 \)
• D. \( 2 \)

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.

Answer 1

The Correct Option is A

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: \( 1 \).