CAT 2023 Slot 1 QA Question 5

Type-in-the-answer (no negative marking) · Algebra · Modulus · Try it, then check the answer and solution below.

The number of integer solutions of equation

2|x|\left(x^{2} + 1\right)=5 x^{2}

TITA Answer:

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: 3

Answer and solution

Answer: 3

📌 Core Concept

The equation involves a modulus function, which requires considering cases for

x \geq 0

and

x < 0

. Additionally, we need to check for integer solutions.

🔢 Step-by-Step Solution

Check

x = 0

Plugging

x = 0

into the equation: $2 \cdot 0 \cdot (0 + 1) = 5 \cdot 0 , which simplifies to $0 = 0

. Thus,

x = 0$ is a solution.

Case 1:

x > 0

Here, \(|x|

Keep going