ECUACIONES DE SEGUNDO GRADO POR FORMULA GENERAL Super facil -Para principiantes

Introduction

This tutorial provides a step-by-step guide on solving quadratic equations using the general formula. Whether you're a beginner or just need a refresher, this guide will help you understand the process and apply it effectively to solve various problems.

Step 1: Understand Basic Concepts

Before diving into solving quadratic equations, familiarize yourself with the key components:

• A quadratic equation is of the form ax² + bx + c = 0, where:

  • a, b, and c are coefficients.
  • x is the variable to solve for.

• The solutions to the quadratic equation can be found using the quadratic formula:

  x = (-b ± √(b² - 4ac)) / (2a)
  

Step 2: Identify Coefficients

For each quadratic equation you want to solve, identify the coefficients:

• Look for numbers in front of x² (a), x (b), and the constant term (c).
• Example: In the equation 2x² + 3x - 5 = 0, the coefficients are:
  • a = 2
  • b = 3
  • c = -5

Step 3: Calculate the Discriminant

The discriminant of the quadratic equation is the part under the square root in the quadratic formula, calculated as:

D = b² - 4ac

• This value helps determine the nature of the roots:
  • If D > 0: Two distinct real roots.
  • If D = 0: One real root (a repeated root).
  • If D < 0: No real roots (complex roots).

Step 4: Apply the Quadratic Formula

Using the values of a, b, c, and the discriminant, apply the quadratic formula:

1. Substitute the values into the formula:

   x = (-b ± √D) / (2a)
   

2. Perform the calculations:
   • Calculate the square root of the discriminant.
   • Calculate both possible values for x by applying the plus and minus.

Step 5: Solve Example Problems

Practice with a few examples:

1. Example 1: Solve 2x² + 3x - 5 = 0

   • Identify coefficients: a = 2, b = 3, c = -5.
   • Calculate D: D = 3² - 4(2)(-5) = 9 + 40 = 49.
   • Apply formula:

     x = (-3 ± √49) / (2 * 2)
     x = (-3 ± 7) / 4
     

   • Solutions: x = 1 and x = -2.5.

2. Example 2: Solve x² - 4x + 4 = 0

   • a = 1, b = -4, c = 4.
   • Calculate D: D = (-4)² - 4(1)(4) = 16 - 16 = 0.
   • Apply formula:

     x = (4 ± √0) / (2 * 1)
     

   • Solution: x = 2 (a repeated root).

Step 6: Review Practice Exercises

After working through examples, tackle additional exercises to reinforce your understanding and skills.

• Practice different quadratic equations, varying coefficients and discriminants.
• Check your solutions and ensure you understand each step taken.

Conclusion

In this tutorial, you learned how to solve quadratic equations using the general formula step-by-step. Key takeaways include understanding the components of quadratic equations, calculating the discriminant, and applying the quadratic formula to find solutions.

As a next step, continue practicing with more complex equations or explore real-world applications of quadratic equations in physics or finance.