Quadratic Equations
Absolute Value Equation — Number of Real Solutions
nta_pyq_2024_apr
Grade 11
Question:
The number of real solutions of the equation $x|x+5|+2|x+7|-2=0$ is
Step-by-Step Solution
Key Concept: Break into cases based on critical points $x=-5$ and $x=-7$. Case I: $x\geq-5$; Case II: $-7<x<-5$; Case III: $x\leq-7$.
3 real solutions: $x=-3,-4,(-3-\sqrt{57})/2$.
Correct Answer: 3