GP011 - Pidge's Academy: Maths Mystery Cache

A small series of caches with a scholastic theme. The final location is not at the listed co-ordinates but is not too far away. The difficulty rating reflects the puzzle and also the hide itself.

1. Cubic equations have three real roots or one real root and two imaginary roots. This one has three real roots, all of which are integers:

x³ +19x² + 28x = 480

First, solve the equation to identify the three roots. Then take the absolute value of each root (i.e. lose any minus signs). Next, if there are any double digit roots, add the two digits together. Finally arrange the three numbers from lowest to highest = FAB.

For example if the three roots are -4, 8, 12 then F would be 3, A would be 4 and B would be 8.

2. Pi, positions 219876 - 219880 counting from the first digit after the decimal point = CDEGH. In case of any ambiguity, the three digits immediately preceding the correct sequence are 285 and the three digits immediately after are 015.

The final location of the cache is at N 51 0A.BCD  W 001 5E.FGH

You can check your answers for this puzzle on GeoChecker.com.