Previous Concepts have presented three methods to solve a quadratic equation:
- By graphing to find the zeros;
- By solving using square roots; and
- By using completing the square to find the solutions
This Concept will present a fourth way to solve a quadratic equation: using the quadratic formula.
History of the Quadratic Formula
As early as 1200 BC, people were interested in solving quadratic equations. The Babylonians solved simultaneous equations involving quadratics. In 628 AD, Brahmagupta, an Indian mathematician, gave the first explicit formula to solve a quadratic equation. The quadratic formula was written as it is today by the Arabic mathematician Al-Khwarizmi. It is his name upon which the word “Algebra” is based.
First, we must make it so one side is equal to zero:
Now it is in the correct form for using the quadratic formula.
- What is the quadratic formula? When is the most appropriate situation to use this formula?
- When was the first known solution of a quadratic equation recorded?
Solve the following quadratic equations using the quadratic formula.