Number of real roots of the equation |x^2+x-6|+2|x|-4=0 is (a) 0 (b) 1 (c) 2 (d) 3

Name: Problem 58, Chapter 2: IIT-JEE Super Course in Mathematics
Uploaded: 2021-09-03T06:32:26-08:00
Duration: 3 min 3 s
Channel: Souad Al Nabulsi
Description: Number of real roots of the equation |x^2+x-6|+2|x|-4=0 is (a) 0 (b) 1 (c) 2 (d) 3

step 1 Greetings also as you see from our question here we need to find the number of the route that we

Number of real roots of the equation |x^2+x-6|+2|x|-4=0 is...

Key Concepts

Absolute Value Function

The absolute value function, defined as |a| = a if a is non-negative and |a| = -a if a is negative, introduces nonlinearity and symmetry into equations. Understanding its properties is essential when it appears in equations, as it means the equation may behave differently over different intervals based on the sign of the expression inside the absolute value.

Piecewise Analysis

When an equation involves absolute value expressions, it can be reformulated into a set of cases where each absolute value expression is replaced by either the expression itself or its negation, depending on the sign of its argument. This method, known as piecewise analysis, allows one to solve the equation over different intervals and ensures all possible scenarios are considered.

Quadratic Functions

Quadratic functions, generally expressed in the form ax² + bx + c, play a crucial role in many algebraic equations. Their properties, such as parabolic shape and discriminant analysis, are useful for determining the number of real roots, especially when they are encapsulated within absolute value signs or interact with other functions.

Number of Real Roots

Determining the number of real roots of an equation involves investigating where the equation equals zero and validating these solutions under the constraints of the problem. Techniques such as case analysis, graphing, or discriminant checks are used to ascertain how many valid real solutions exist.

Transcript

Please give Ace some feedback