Steel VIG (January 30-February 1, 2009)

February 3, 2009

John Steel was one of my advisors at UC Berkeley. The fifteenth Very Informal Gathering of Logicians at UCLA (VIG) was in honor of John Steel on his 60th birthday.

The meeting was excellent, with some very interesting talks and nice shared memories. Plus, Benjamin Miller worked miracles and secured the photo above without John finding out.

305 -Solving cubic and quartic polynomials (2)

February 3, 2009

Let’s return to the problem of solving quartic polynomials. In the first lecture on this topic, we reduced the problem of solving an equation like

$x^4+ax^3+bx^2+cx+d=0$

to solving the similar problem

$y^4+py^2+qy+r=0,$

in which the coefficient of $y^3$ is zero. This is achieved by a simple translation, simply set $x=y-a/4$. This was motivated and explained in that lecture. Let us now see how we can approach this problem.