Polygon 42

Which polygon has 42 more diagonals than sides?

Correct result:

n =  12

Solution:

12n(n−3)=n+42 n2−5n−84=0  a=1;b=−5;c=−84 D=b2−4ac=52−4⋅1⋅(−84)=361 D>0  n1,2=−b±D2a=5±3612 n1,2=5±192 n1,2=2.5±9.5 n1=12 n2=−7   Factored form of the equation:  (n−12)(n+7)=0   n>0 n=12

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