A rectangular plot has perimeter 46 m and area $120{\text{m}}^2$.
Which quadratic polynomial (leading coefficient 1) has the plot’s length and breadth as its zeroes?

Perimeter $2(l+b)=46$ gives the sum $l+b=23$; the area gives the product $lb=120$. The polynomial is $x^2-(l+b)x+lb=x^2-23x+120$. (Its zeroes are 8 and 15, and 8 + 15 = 23 with $8\times 15=120.)x^2-46x+120$ uses the perimeter itself as the sum; $x^2+23x+120$ forgets the minus in $-(l+b)$; $x^2-23x-120$ flips the sign of the product.