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Exercising Quadratic Equations

Jul 11, 2024

Exercising Quadratic Equations

Introduction

  • Instructor: рдкрд╡рди
  • Topic: Exercise 4 on quadratic equations.
  • Recap: Covered examples and Exercise 4.1 in previous classes.

Standard Form of Quadratic Equation

  • Quadratic Equation Standard Form: ax┬▓ + bx + c = 0
  • Tasks: Convert given forms to standard quadratic form.

Examples from Exercise 4.1

First Question

  1. Checking if Equations are Quadratic
  • Transform the given expressions to standard quadratic form.
    1. x┬▓ - y = 0 is quadratic.
    2. x┬▓ - y = 0 is quadratic.
    3. x┬▓ + 3x + 1 = (x-2)┬▓
  • Results in a quadratic equation.
  1. Broke down to Standard Form
    • Simplify and verify quadratic form.
  2. Transform Left-hand Side
    • Confirm transformations.
  3. Identify Quadratic
    • Verify resulting form.

Second Question

  1. Form Quadratic from Rectangle Area
  • Problem Statement: Area = 528m┬▓, find length and breadth.
  • Approach: Let breadth = x, Length = 2x.
  • Solve quadratic generated from Area formula.

Third Question

  1. Rectangular Plot - Solving Equation
  • Problem Statement: Find positive integers.
  • Solve using given sum and product.

Fourth Question

  1. Train Speed and Time
  • Problem Statement: Distance = 480 km, speed = x.
  • Create equation: Use distance = speed * time formulation.
  • Solve quadratic from speed changes described.

Quadratic Equation Factorization Examples

First Example (Factorization Method)

  • Given: x┬▓ - 5x - 6=0
  • Factorize to find roots.
  • Use: ax┬▓ + bx + c = 0

Second Example

  • Given: 2x┬▓ + x - 6 =0
  • Find roots using factorization.

Third Example

  • Given: тИЪ2x┬▓ + 7x + 5тИЪ2 = 0
  • Use: Standard form conversion.
  • Factorization for roots.

Remaining Examples

  • Same approach using different numerical values.
  • Always standardize form then solve.

Practice Problems

Example Problems from Book

  • Questions provided in the session had practical applications like production cost, number of items, etc.
  • Solving these required creating and solving quadratic equations.

Solving using Nature of Roots (Upcoming Topic)

  • Next Class: 4.3 exercises, focusing on root nature.

Summary of Learnings

  • Importance of converting equations to standard quadratic form.
  • Using factorization methods to solve them.
  • Practical application problems help reinforce concepts.

If any questions, doubts please ask in comments.

Full transcript