4. QUADRATIC EQUATIONS

4. QUADRATIC EQUATIONS

  • 4

    Quadratic Equations

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

  • 4.1

    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.

    • Key Summary

    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.

    Key Takeaways

    • 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.