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The fundamental theorem of algebra

A cache by drsolly Send Message to Owner Message this owner
Hidden : 09/17/2007
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Geocache Description:

We all learned the general solution of the quadratic equation at school. But did you learn how to extract the roots of a cubic equation? There is a general solution for the cubic. Read it and weep.

Quartic equations are, of course, even worse - you have to convert to a depressed quartic, and then use Ferrari's solution. Feeling depressed yet?

When you move up to quintic equations, it starts getting really tricky, they're only solvable if the Galois group is a solvable group. It's a mess. Galois died when he was 20, in a duel.  

But don't worry about any of that. Because I'm not giving you a quadratic, a cubic, a quartic or even a quintic. What I'm giving you is so horrible, it doesn't even have a name, although if it did, it would be a hexic or maybe a sexic? I like "sexic". So, here's your sexic equation.

x6 - 32x5 + 415x4 - 2780x3 + 10084x2 - 18608x + 13440 = 0

If you remember the fundamental theorem of algebra, then you'll know that this gives you six solutions. Arrange them in increasing sequence, and call then abcdef. Then the cache is at N 51° 43.caf W 000° 39.bde

But before you rush off to retreive it, you'll need some Special Equipment - a Phillips head screwdriver.

First to find - Bob Smith

Additional Hints (Decrypt)

[Puzzle]Vg'f abg nf qvssvpyg nf vg ybbxf

Decryption Key


(letter above equals below, and vice versa)