06/11/2025
THE QUADRATIC EQUATION
A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where 'a' is not equal to zero. It can be solved using methods like factoring, completing the square, or the quadratic formula, which is
x = [-b ± √(b² - 4ac)] / 2a.
Standard form
The standard form is ax² + bx + c = 0.
a, b, and c: are known numbers (coefficients and constant).
x: is the variable you are solving for.
The condition a ≠ 0 is crucial, as it distinguishes a quadratic equation from a linear one.
HOW TO SOLVE A QUADRATIC PROBLEM
➡️Factoring:
This method works when the quadratic expression can be factored into two binomials. The solutions are found by setting each factor to zero.
➡️Quadratic Formula:
This formula provides a solution for any quadratic equation and is often the most reliable method.
x = [-b ± √(b² - 4ac)] / 2a
The part under the square root, b² - 4ac, is called the discriminant and tells you about the nature of the solutions.
➡️Completing the Square:
This is a method that involves manipulating the equation to create a perfect square trinomial, which can then be solved by taking the square root of both sides.
➡️Graphical method
Number of solutions
A quadratic equation will always have two solutions, which can be real or complex.
The discriminant (b² - 4ac) determines the type of solutions:
•Positive discriminant: Two distinct real solutions.
•Zero discriminant: One real solution (a repeated root).
• Negative discriminant: Two complex solutions.
