Sets, Relations & Functions
Number of Solutions (Graphical)
nta_pyq_2025_apr
Grade 11
Question:
The number of real solution(s) of the equation $x^2 + 3x + 2 = \min\{|x-3|, |x+2|\}$ is:
Step-by-Step Solution
Key Concept: Graph both sides: LHS is an upward parabola with vertex at $(-3/2, -1/4)$; RHS is a piecewise linear function. Count intersections graphically.
LHS $= (x+3/2)^2 - 1/4$. RHS $\geq 0$. The parabola crosses RHS at 2 points (verified graphically). Number of solutions $= 2$.
Correct Answer: 2