The number of real solution(s) of the equation is : [2025]

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Solution

Q.
The number of real solution(s) of the equation $x^{2} + 3 x + 2 = \min {| x - 3 |, | x + 2 |}$ is : [2025]

1 2

2 3

3 1

4 0

Ans.
(1)

$In (- \infty, \frac{1}{2})$ , $| x + 2 |$ is minimum and in $(\frac{1}{2}, \infty)$ , $| x - 3 |$ is minimum.

From the graph, only two solutions.

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