Problems Leading to Quadratic Equations

Word problems

Many problems give two unknowns but only one equation if you substitute. Common types:

1. Consecutive numbers: x and x+1

2. Area problems: Length = x, width = x-3, area = 40   ⇒   x(x-3) = 40

3. Age problems: Current ages, then ages in 5 years

Example: The product of two consecutive positive integers is 72. Find them.
Let numbers be x and x+1.
x(x+1) = 72
x² + x - 72 = 0
(x+9)(x-8) = 0
x = 8 (reject -9 as not positive)
Numbers are 8 and 9.

Always check if both solutions make sense in context.

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