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JEE Main 202524 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
24 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2025 · 24 January · Evening Shift · Mathematics · Functions

The number of real solution(s) of the equation x^2+3 x+2= \...

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

Options

  1. A1
  2. B0
  3. C2
  4. D3

Correct answer

C. 2

Step-by-step solution

x2+3x+2=min⁡{∣x−3∣,∣x+2∣}x^2+3 x+2=\min \{|x-3|,|x+2|\}y=x2+3x+2y=x2+2(32)x+94−94+2y=(x+32)2−14y+14=(x+32)2⇒ Parabola vertex (−32,−14)\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
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