Quadratic Equations
Absolute Value Equation — Number of Real Roots
nta_pyq_2023_apr
Grade 11
Question:
The number of real roots of $x|x|-5|x+2|+6=0$ is
Step-by-Step Solution
Key Concept: Split into 3 cases: $x<-2$, $-2\leq x<0$, $x\geq0$. Each gives a quadratic; find valid roots in each region.
3 real roots.
Correct Answer: 4