Understanding Quadratic Equations:

0
6K
  • A quadratic equation is a polynomial equation of degree 2. It can be expressed in the general form:
    ax² + bx + c = 0
    
    where a, b, and c are constants, and a ≠ 0.

Methods for Solving Quadratic Equations:

  1. Factoring:

    • Factor the quadratic expression into two linear factors.
    • Set each factor equal to zero and solve for x.
    • Example:
      x² - 5x + 6 = 0
      (x - 2)(x - 3) = 0
      x = 2 or x = 3
      
  2. Completing the Square:

    • Convert the quadratic equation into a perfect square trinomial.
    • Take the square root of both sides and solve for x.
    • Example:
      x² - 6x + 2 = 0
      x² - 6x + 9 = 7
      (x - 3)² = 7
      x - 3 = ±√7
      x = 3 ± √7
      
  3. Quadratic Formula:

    • Apply the quadratic formula:
      x = (-b ± √(b² - 4ac)) / (2a)
      
    • Substitute the values of a, b, and c from the quadratic equation.
    • Simplify and solve for x.

Example:

Solve the equation: 2x² - 3x - 5 = 0

Method 1: Factoring

  • We cannot factor this equation into two linear factors.

Method 2: Completing the Square

  • Divide the equation by 2 to simplify:
    x² - (3/2)x - (5/2) = 0
    
  • Add (3/4)² to both sides to complete the square:
    x² - (3/2)x + (9/16) = (9/16) + (5/2)
    (x - 3/4)² = 49/16
    x - 3/4 = ±7/4
    x = 3/4 ± 7/4
    x = 5/2 or x = -1
    

Method 3: Quadratic Formula

  • Substitute a = 2, b = -3, and c = -5 into the formula:
    x = (-(-3) ± √((-3)² - 4(2)(-5))) / (2(2))
    x = (3 ± √49) / 4
    x = (3 ± 7) / 4
    x = 5/2 or x = -1
    

Choosing the Best Method:

  • Factoring is often the quickest method if it's possible.
  • Completing the square is useful when the quadratic equation is not easily factored.
  • The quadratic formula is always applicable, even if factoring or completing the square is difficult.

I hope this explanation helps! Feel free to ask if you have any more questions.

Like
Love
2
Search
Categories
Read More
Technology
The Ten Commandments of Computer Ethics
The Ten Commandments of Computer Ethics were created by the Computer Ethics Institute to guide...
By Olaim 2024-07-16 17:02:40 0 6K
Technology
History of Python and Computer Hardware
As computer programming started to get popular and evolve in the 1960’s and 70’s,...
Computer Programming
Range and Nested Loops
Range Function (range()) The range() function is a built-in function in Python used to generate...
Education
A MUST KNOW FOR A'LEVEL HISTORY STUDENTS
https://acrobat.adobe.com/id/urn:aaid:sc:EU:7c45002b-2e38-426f-a0b9-8447c474993b
By Expedito 2024-07-15 19:08:17 0 7K