Solve [x^2+x+1]=2 ([ ] denotes Greatest Integer Function). |...

Name: Problem 404, Chapter 7: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2022-01-10T02:03:35-08:00
Duration: 3 min
Channel: Aman Gupta
Description: Solve [x^2+x+1]=2 ([ ] denotes Greatest Integer Function).

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Key Concepts

Greatest Integer Function

The greatest integer function, also known as the floor function, maps any real number to the largest integer that is less than or equal to that number. It is essential in problems where rounding behavior is incorporated into equations, requiring the establishment of specific intervals for the input expression.

Inequality Analysis

When an equation involving the floor function is given, it is necessary to translate the equation into an inequality. This involves establishing that the inner expression must lie between an integer and the next integer. Proficiency in setting up and solving such inequalities is crucial for isolating the variable and determining valid solutions.

Quadratic Functions

Quadratic functions are polynomial functions of degree two and are characterized by their parabolic graphs. Understanding their properties, such as the vertex, axis of symmetry, and discriminant, is important when they appear within more complex functions, as these properties help determine the range of values the quadratic expression can attain.

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