Quadratic Equations One Shot Lecture Notes

Instructor: कुल्दी बंडारी
Class: 9th and 10th
Duration: 20 minutes

Session Overview

• Objective: Comprehensive understanding of quadratic equations in 20 minutes
• Importance: Recap of the entire chapter useful for exams

Schedule Overview

• Weekly schedule presented; prior sessions reviewed
• Encourage joining the official Telegram group for updates

Quadratic Equation Introduction

• Definition:
  A quadratic equation is an equation where the highest power of the variable is 2.

• General Form:
  [ ax^2 + bx + c = 0 ]

  • a cannot equal 0; if a = 0, the equation becomes linear.

Key Topics to Cover

1. Definition and General Form of Quadratic Equation
2. Solution by Factorization Method
3. Quadratic Formula
4. Nature of the Roots

Key Concepts

Roots of Quadratic Equations

• Roots (α and β):
  • Reciprocal relationship mentioned (if α = 2, then β = 1/2)
• Product of Roots:
  [ ext{Product} = \frac{c}{a} ]
  • In this example, c = k and a = 1
  • k = 5 derived.

Solution Methods

• Factorization Method:
  • Known as middle term splitting.
  • Example problem:
    [ x^2 - 18x + 77 = 0 ]
  • Factored as [ (x - 11)(x - 7) = 0 ]

Quadratic Formula

• Formula:
  [ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]
• Derived from the quadratic equation's standard form.
• Example with a discriminant calculation provided.

Nature of Roots

• Discriminant ( D) determines the nature of the roots:
  • D < 0: Imaginary roots
  • D = 0: Real and equal roots
  • D > 0:
    • Rational and unequal roots if D is a perfect square
    • Irrational roots if not a perfect square

Note: Care when applying the quadratic formula and identifying nature of roots to ensure thorough understanding and correct calculations.

Conclusion

• Reviewed essential topics of quadratic equations
• Emphasis on practice and understanding the methods to solve problems effectively.

Reminder:

• Don't forget to review and practice beyond the session!