Math Club, November 15.

Speaker: Sean Sather-Wagstaff

Title: Solving polynomial equations... or not

Abstract: In high school algebra, we all learn how to solve linear equations (ax+b=0) and quadratic equations (ax^2+bx+c=0). In particular, the quadratic formula, gives a closed form solution to arbitrary quadratic equations in terms of elementary operations: sum, difference, product, quotient, and roots. It is not usually taught that similar formulas exist for cubic (degree 3) and quartic (degree 4) equations. I will discuss these formulas along with the fact that it is impossible (!) to find such formulas for equations of degree 5 and higher.