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4. QUADRATIC EQUATIONS

The chapter delves into quadratic equations, exploring their forms, roots, and various methods of solving them. It illustrates real-life applications of quadratic equations, enriches the understanding of their properties, and highlights the significance of the discriminant in determining the nature of roots. A series of exercises and activities help in consolidating the concepts explained.

Sections

QUADRATIC EQUATIONS

This section introduces quadratic equations, their forms, significance, and various methods for finding their roots, along with applications in real-life scenarios.

4 Section Overview

Start current section content and materials

4.1 Introduction

This section introduces quadratic equations and their real-life applications, emphasizing their historical significance and foundational concepts.

4.2 Quadratic Equations

This section introduces quadratic equations, their standard form, and examples of their applications in real life.

4.3 Solution of a Quadratic Equation by Factorisation

This section covers the process of solving quadratic equations through factorization, including examples and methods to identify roots.

4.4 Nature of Roots

This section discusses the nature of roots of quadratic equations based on their discriminants.

4.5 Summary

This section summarizes the key concepts related to quadratic equations, including their standard form, roots, and methods to solve them.

Learning Objectives

  • A quadratic equation is an equation of the form ax² + bx + c = 0 where a, b, and c are real numbers and a ≠ 0.

  • The solutions of quadratic equations can be found using factorization, completing the square, or the quadratic formula.

  • The discriminant of a quadratic equation determines the nature of its roots: two distinct real roots, one repeated real root, or no real roots.

Key Concepts

Quadratic Equation

An equation of the form ax² + bx + c = 0 where a, b, and c are constants, and a ≠ 0.

Discriminant

The expression b² - 4ac that indicates the nature of the roots of a quadratic equation.

Roots of a Quadratic Equation

The values of x that satisfy the equation ax² + bx + c = 0, which can be real or complex numbers.

Practice Exercises

Total Questions

3

Estimated Time

6 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting