Quadratic Word Problems
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Many real problems lead to a quadratic equation: when two unknown lengths are multiplied, when everyone plays everyone else, or when journey times are compared. The method is always the same: choose the unknown, form the equation, solve it and check which roots make sense in the problem.
What does this generator do?
On the easy level you work with the product of two consecutive numbers and a rectangle with a known area. On the medium level you find the number of teams in a tournament, the vertices of a polygon from its diagonals and the sides of a right-angled triangle. On the hard level you solve problems about a path round a garden, a cyclist’s speed and a rectangle with known perimeter and area.
How to use it
1) Choose the unknown, for example the shorter side x. 2) Write the other quantities in terms of x. 3) Form the equation and rearrange it to ax² + bx + c = 0. 4) Solve it. 5) Reject a negative root for a length, a count or a speed. 6) Answer the question.