Transcription
Quadratic, cubic, andquartic equationsBy: David Panson
Quadratic Equations Equations with an X2 set to 0 General formula for the equation isax2 bx c 0 General Equation for solution is
Cubic Equations Equations with an X3 set to 0 General formula for the equation isax3 bx2 cx d 0
Quartic Equations Equations with an X4 set to 0 General formula for the equation isax4 bx3 cx2 dx e 0
The Challenge Solve with basic operations that cancel andprevent the use of mind blowing math in a precalculator era Be able to account for negatives and zeros Make a uniform way to solve all variations ofeach problem
Solutions Quartic and Cubic– Roots! Quadratic– Factoring– Quadratic formula– Completing the square
Use Today Math class? And .yeah. Quadratic, cubic, and quartic problems aresolved still so they most matter right? They are needed to understand accelerationof cars, planes, football players, or whateverelse, air flow and flight, cell phone signaltechnology, and tons of other stuff. Like math in general they can be found mostanywhere. Even hiding in science.
Timeline 400 BC Sumerians Start algorithmic thoughts 300 BC Euclid and his geometry stuff 600 AD Brahmagupta finds out he can have less than 0 friends (but onlyin India.) 800 Al Khwarizmi and his 6 class acts1145 Savasorda and his best friend. A book.1494 Luca Pocioli spreads Suma knowledge1515ish Scipione dal Ferro looks at a half full cup. But he thinks itsfull. 1526 Ferro finally shares his secret with a stupid genius (Fior)1545 Cardan breaks the bro code. Politely. But Tartaglia is still sad.1567 Stifel does a magic trick. Nerd style.1637 Descartes makes it FBO or you know. at least O.1673 Leibniz proves that centuries of work is in fact not useless.
Al Khwarizmi’s Classificationsof Quadratics Squares equal to roots. Squares equal to numbers. Roots equal to numbers. Squares and roots equal to numbers, e.g. x2 10x 39. Squares and numbers equal to roots, e.g. x2 21 10x. Roots and numbers equal to squares, e.g. 3x 4 x2.
FiorVS Tartaglia 30 Problems to be solved in 50 days. Fior issued the challenge Tartaglia solves all problems super fast(like a boss)– They were all x3 mx2 n form
Timeline for People that aren’t me 400 BC Sumerians Start algorithmic problem solving300 BC Euclid used geometry to answer some quadratics600 AD Brahmagupta finds near modern methods but only in India800 Al Khwarizmi and indentifies 6 classifications of quadratics.1145 Savasorda published Liber Embadorum first publishedquadratic method1494 Luca Pocioli published Suma unified previous knowledge1515ish Scipione dal Ferro solves cubics but only some.1526 Ferro finally shares his secret solution with Fior1545 Cardan published Ars Magna and Tartaglias cubic equation1567 Stifel condensed previous knowledge into the quadraticequation1637 Descartes published La Giometrie with the modern formula.1673 Leibniz proves the equation with a purely algebraic proof.
Works by smarter people Quadratic etc equations.html uation-part-ii http://dwick.org/pages/cubicquartic.pdf r.pdf http://en.wikipedia.org/wiki/Quadratic equation
A book. 1494 Luca Pocioli spreads Suma knowledge 1515ish Scipione dal Ferro looks at a half full cup. But he thinks its full. 1526 Ferro finally shares his secret with a stupid genius (Fior) 1545 Cardan breaks the bro code. Politely. But Tartaglia is
