Sets, Relations & Functions
Absolute Value Equation — Number of Real Solutions
nta_pyq_2026_jan
Grade 11
Question:
The number of distinct real solutions of the equation $x|x+4|+3|x+2|+10=0$ is
Step-by-Step Solution
Key Concept: Critical points $x=-4,-2$. Case 1 ($x\geq-2$): $x^2+7x+16=0$, discriminant $<0$. Case 2 ($-4\leq x<-2$): $x^2+x+4=0$, discriminant $<0$. Case 3 ($x<-4$): $x^2+7x-4=0$.
1 distinct real solution.
Correct Answer: 2