if there are n teams in a league and each team plays each other twice in a season, the total number of games is given by the polynomial n^2-n=N. a women's basketball league plays a total of 90 games. how many teams are in the league
n^2 -n can be factorized as n (n-1), so we have to solve
n(n-1) = 90
Remembering that n is a whole number , we have to find two consecutive whole numbers that multiply to give 90
Answer 10 *9 = 90 so there are 10 teams
That was the easy way, but more mathetical is to write it in standard form and factorize
n^2 -n -90 =0
n^2 -10n + 9n -90 =0
n(n-10) + 9 (n -10) =0
(n-10)(n +9) =0
n-10 =0 or n+9 =0
n= 10 or -9
Since number of teams cannot be negative, n =10
There are 10 teams
Hi , Jacqueline .
Is it OK - I've given you two methods to check that the answer is correct- second way is more mathematical but the other confirms it
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