Question

The function f(x)=x^2-x can be used to model the total number of games played in one season of the league, where is the number of teams. If there were 132 games played in one season, what is the total number of teams in the league?

Answer 1

To find the total number of teams in the league, we need to solve the equation f(x) = x^2 - x = 132.

x^2 - x = 132
x^2 - x - 132 = 0

We can factor this equation as:
(x - 12)(x + 11) = 0

This gives us two possible solutions:
x = 12
x = -11

Since the number of teams cannot be negative, we ignore the solution x = -11.

Therefore, the total number of teams in the league is 12.