In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained by him in the two subjects separately.
Let the marks obtained by P in mathematics and science be x and (28 – x) respectively
According to the given condition,
(x + 3)(28 – x – 4) = 180
(x + 3)(24 – x) = 180
– x2 + 21x + 72 = 180
x2 – 21x + 108 = 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 = – 21 c = 108
= 1.108 = 108
And either of their sum or difference = b
= – 21
Thus the two terms are – 12 and – 9
Difference = – 12 – 9 = – 21
Product = – 12. – 9 = 108
x2 – 12x – 9x + 108 = 0
x (x – 12) – 9 (x – 12) = 0
(x – 12) (x – 9) = 0
(x – 12) = 0 or (x – 9) = 0
x = 12, x = 9
When x = 12,
28 – x = 28 – 12 = 16
When x = 9,
28 – x = 28 – 9 = 19
Hence he obtained 12 marks in mathematics and 16 science or
He obtained 9 marks in mathematics and 19 science.