Chapter: Quadratic Equations· Mathematics Part 1 (Algebra)
Answer: Son 9 years, father 36 years
Let the son’s present age be \(x\); father’s age \(= 45 - x\).
Five years ago: son \(x - 5\), father \(40 - x\).
\((x - 5)(40 - x) = 124\)
\(40x - x^2 - 200 + 5x = 124\)
\(x^2 - 45x + 324 = 0\)
\(\Delta = 2025 - 1296 = 729 = 27^2\); \(x = \dfrac{45 \pm 27}{2} = 36\) or \(9\).
If \(x = 36\), the father would be 9, which is impossible. So son \(= 9\) years, father \(= 36\) years.
Check: five years ago \(4 \times 31 = 124\) ✓.