Mr. P's teenaged girlfriend Miss Q is a student of mathematics. Miss Q brought a well framed crochet with a polynomial in X ( having integer coefficients ) stitched on it as the birthday present on his birthday sometime this year. The polynomial is so constructed that one of its roots is equal to Mr. P's age ( in years) on his birthday (this year).

Someone present at the birthday party tried to find its root, not being aware that the root stood for the age of the host. He substituted X=8, which gave him 64. He tried a different number slightly greater than 8 but less than 16, which gave him 70.

If Mr. P is older than his 16- year old girlfriend, how old was he on his birthday this year?

The following polynomial satisfies the requirements of this puzzle:
 -2x² + 40x - 128

Substituting X=8 gives 64, and substituting X=9 gives 70.
The roots for this polynomial are 4 and 16.
If Mr. P was born in January and Miss Q in February of the same year, for example, both Mr. P and Miss Q could be 16 years old, and, yet, Mr. P would also,  this year, be older than his girlfriend.

Edited on March 3, 2007, 6:55 am

Posted by Dej Mar on 2007-03-03 06:24:03