This cheat sheet covers the high school math concept – Quadratic Equations.
An equation of the form ax2 + bx + c = 0 (where a ≠ 0) is known as a quadratic equation. The values of the variable that satisfy the equation are called the roots of the equation. A quadratic equation always has two roots, which may be real or imaginary, depending upon the values of a, b, and c.
Babylonian mathematicians, as early as 2000 BC, could solve problems relating the areas and sides of rectangles. The problems typically involved solving a pair of simultaneous equations of the form : x + y = p, xy = q, which are equivalent to the equation x2 – px + q = 0. In 628 AD, Brahmagupta, an Indian mathematician, gave the first explicit solution of the quadratic equation ax2 + bx = c. In 1637, René Descartes published La Geometrie containing the quadratic formula in the form we know today.
A good knowledge of plotting graphs of functions will help quite a bit in solving problems related to quadratic equations. Cheat sheets on Graph Transformations (Basic and Advanced) are also available on this website.
This one page PDF covers summarised theory and the most important formulas related to the concept. Keep it handy while you’re revising the concept, especially before an exam.
The topics included in this cheat sheet are:
- Nature of Roots of Quadratic Equations
- Real and Distinct Roots
- Real and Equal Roots
- Imaginary Roots
- Rational Roots
- Integral Roots
- Relation Between Roots and Coefficients
- Common Roots
- Range of a Quadratic Function
- Sign of a Quadratic Function
- Graph of a Quadratic Function
- Location of the Roots of Quadratic Equations
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