Chapter 4: Quadratic Equations

Example – 12. Is the following situation possible? If so, determine their present ages.

The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Solution :- Let present age of one friend be x and that of the other 20 – x.

4 years ago age of first friend = x – 4, and that of the other = 20 – x – 4 = 16 – x.

According to question,  (x – 4 )(16 – x ) = 48

Or, 16x – x² – 64 + 4x =48

Or, x² + 20x – 112 = 0

Or, x² – 20x + 112 = 0

Here, a = 1, b = – 20, c = 112

D = b² – 4ac = (– 20 )² – 4 ×1 × 112 = – 48 < 0.

Hence, the given situation is not possible.