The sum of the ages of a boy and his brother is 25 years, and the product of their ages in years is 126. Find their ages.
Let the present age of boy and his brother be x years and (25 – x) years
According to given question
x(25 – x) = 126
25x – x2 = 126
x2 – 25x + 126 = 0
Using the splitting middle term – the middle term of the general equation 
is divided in two such values that:
Product = a.c
For the given equation a = 1 b = – 25 c = 126
= 1.126 = 126
And either of their sum or difference = b
= – 25
Thus the two terms are – 18 and – 7
Sum = – 18 – 7 = – 25
Product = – 18. – 7 = 126
x2 – 18x – 7x + 126 = 0
x (x – 18) – 7(x – 18) = 0
(x – 18) (x – 7) = 0
x = 18 or x = 7
x = 18 (Present age of boy cannot be less than his brother)
if x = 18
The present age of boy is 18 years and his brother is (25 – 18) = 7years