Question

$$ \text { Solve for }[x]^{2}-2[x]-8=0 $$

Name: Problem 25, Chapter 1: Differential Calculus Booster with Problems and Solutions for JEE Main and Advanced
Uploaded: 2022-02-25T18:10:55-08:00
Duration: 1 min 38 s
Channel: Varsha Aggarwal
Description: Solve for [x]^2-2[x]-8=0

   $$
\text { Solve for }[x]^{2}-2[x]-8=0
$$

Differential Calculus Booster with Problems and Solutions for JEE Main and Advanced

Rejaul Makshud 2019 Edition

Chapter 1, Problem 25

Instant Answer

Solved by Expert Varsha Aggarwal

02/25/2022

Step 1

Here, $[x]$ denotes the greatest integer less than or equal to $x$. Show more…

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$$ \text { Solve for }[x]^{2}-2[x]-8=0 $$

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Key Concepts

Zero Product Property

The zero product property states that if the product of two expressions is zero, then at least one of the expressions must be zero. This principle is essential in solving factored quadratic equations, as it allows for the separation of the equation into simpler linear equations.

Factoring Quadratic Polynomials

Factoring involves rewriting a quadratic expression as a product of two binomials. This technique simplifies the equation and makes it possible to apply the zero product property to find the solutions of the variable.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation, generally expressed in the form ax² + bx + c = 0. Solving these equations often involves methods such as factoring, completing the square, or applying the quadratic formula, which are fundamental techniques in algebra.

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