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application of Quadratic equations

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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

Mar 18th, 2015

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

Mar 18th, 2015

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

Mar 18th, 2015

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