Quadratic Applications

Question

. The number of baseball games that must be scheduled in a league with n teams is

given by G(n) = where each team plays every other team exactly once. A league 2

n −n

2

schedules 15 games. How many teams are in the league?

● To get your started, let G(n) be 15 and then solve the quadratic equation.

Answer 1

The number of games with n teams with no repetition and no order importance is "n choose 2" or 1/2*n*(n-1).

Since the number of games is already given, then

1/2*n*(n-1) = 15 or n²-n-30=0. A positive solution of this equation is 1/2*(1+√121) = 6.

There are 6 teams in the league.