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

Question

Aicharya · Accepted Answer

$x^2+3 x+2=\min \{|x-3|,|x+2|\}$

$\begin{aligned}
& y=x^2+3 x+2 \\ & y=x^2+2\left(\frac{3}{2}\right) x+\frac{9}{4}-\frac{9}{4}+2 \\ & y=\left(x+\frac{3}{2}\right)^2-\frac{1}{4} \\ & y+\frac{1}{4}=\left(x+\frac{3}{2}\right)^2 \\ & \Rightarrow \text { Parabola vertex }\left(\frac{-3}{2}, \frac{-1}{4}\right)
\end{aligned}$
$\Rightarrow$ By graph 2 solution possible

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

Solution