The Quadratic Equation

The Quadratic Equation

The quadratic equation formula describes the general shape of a parabola, and the coefficients a, b, and c determine its size and position.



The formula to solve a quadratic equation is very simple. Almost all high-school students should know this.



The discriminant part indicates whether the solutions of x will be real or imaginary.

Discriminant > 0

When the discriminant is a positive number, there are two real roots to the equation, given by the formulas shown above.

Discriminant = 0

When the discriminant is equal to zero, there is only one real solution.

Discriminant < 0

When the discriminant is negative, there are no real roots, and two imaginary roots, as shown above. The roots form a complex conjugate pair.


Here is a very simple pub type question and answer, ideal for the so-called “educated” educators. Very few in UK can answer this one correctly.


Who was the first person to give an explicit solution for a quadratic equation with negative numbers?



Question and Answer

Here are some real-life example questions and answers. Consider these as online worksheets. It might prove useful to GCSE students and teachers.

Quadratic Equation Example Using Completing the Square Method
Quadratic Equation Example Using Quadratic Formula
Quadratic Equation Turning Point Formula Example
Quadratic Equation Area Problems
Quadratic Equations Fractions
Quadratic Equation Area of Rectangle

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