Quadratic Equations
Absolute Value Inequalities
JEE Main 2021
Grade 11
Question:
The number of integer solutions of $x^2 + 3|x| - 10 < 0$ is:
(1) $2$
(2) $3$
(3) $4$
(4) $6$
Step-by-Step Solution
Key Concept: Let $t = |x| \geq 0$ and factor: $(|x| + 5)(|x| - 2) < 0$. Find the range of $|x|$, then convert back to $x$ and count integer solutions.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)