




Quadratic Equations  The Quadratic Formula
Each topic includes lecture notes with an interactive demonstration, a video, and testing content.


How to Teach with these Materials

Motivation 

The ancient Egyptians and Greeks knew how to solve some quadratic equations.
The Italian mathematician Tartaglia found the formula for solving cubic
(3^{rd} degree) equations in about 1545. Almost immediately after that, another
Italian mathematician, Ferrari, derived the formula for solving quartic (4^{th} degree) equations.
Around 1832, the French mathematician Evariste Galois proved that for polynomials of degree 5
or higher, the situation is hopeless: There is no formula involving only the coefficients and
algebraic operations (including the extraction of roots) that can find the roots of all 5^{th}
degree polynomials, or of all 6^{th} degree polynomials, or ...
Galois died in a duel, allegedly involving a woman and possibly a French royalist
conspiracy to dispose of a strong Republican supporter. He was only 20 when he died, but
the consequences of his mathematical genius are still being felt today.










