Dror Bar-Natan: Classes: 2003-04: Math 157 - Analysis I: (32) Next: Homework Assignment 8
Previous: Class Notes for Thursday October 23, 2003

Monsters

See also: Monsters.nb, Monsters.pdf

The linear equation and a tame formula:

In[1]:=

Solve[a x + b == 0, x]

Out[1]=

{{x -> -b/a}}

The quadratic equation and the monster:

In[2]:=

Solve[a x^2 + b x + c == 0, x] // First

Out[2]=

{x -> (-b - (b^2 - 4 a c)^(1/2))/(2 a)}

The cubic equation and the horrible monster:

In[3]:=

Solve[a x^3 + b x^2 + c x + d == 0, x] // First

Out[3]=

{x -> -b/(3 a) - (2^(1/3) (-b^2 + 3 a c))/(3 a (-2 b^3 + 9 a b c - 27 a^2 d + (4 (-b^2 + 3 ... c - 27 a^2 d + (4 (-b^2 + 3 a c)^3 + (-2 b^3 + 9 a b c - 27 a^2 d)^2)^(1/2))^(1/3)/(3 2^(1/3) a)}

The quartic equation and the truly horrible monster:

In[4]:=

Solve[a x^4 + b x^3 + c x^2 + d x + e == 0, x] // First

Out[4]=

{x -> -b/(4 a) - 1/2 √ (b^2/(4 a^2) - (2 c)/(3 a) + (2^(1/3) (c^2 - 3 b d + 12 a e))/ ... (c^2 - 3 b d + 12 a e)^3 + (2 c^3 - 9 b c d + 27 a d^2 + 27 b^2 e - 72 a c e)^2)^(1/2))^(1/3)))))}

The quintic equation; we're dead now:

In[5]:=

Solve[a x^5 + b x^4 + c x^3 + d x^2 + e x + f == 0, x] // First

Out[5]=

{x -> Root[f + e #1 + d #1^2 + c #1^3 + b #1^4 + a #1^5 &, 1]}

Converted by Mathematica  (October 23, 2003)