In a class test, the sum of Kamal's marks in mathematics and English is 40. Had he got 3 marks more in mathematics and 4 marks less in English, the product of the marks would have been 360. Find his marks in two subjects separately.
Let Kamal's marks in mathematics and English be x and y, respectively
According to the question
x + y = 40 – – – – – – – (1)
Also (x + 3)(y – 4) = 360
(x + 3)(40 – x – 4) = 360 from (1)
(x + 3)(36 – x) = 360
36x – x2 + 108 – 3x = 360
33x – x2 – 252 = 0
x2 – 33x + 252 = 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 = – 33 c = 252
= 1. – 252 = 252
And either of their sum or difference = b
= – 33
Thus the two terms are – 21 and – 12
Sum = – 21 – 12 = – 33
Product = – 21. – 12 = 252
x2 – 33x + 252 = 0
x2 – 21x – 12x + 252 = 0
x(x – 21) – 12(x – 21) = 0
(x – 21) (x – 12) = 0
(x – 21) = 0 or (x – 12) = 0
x = 21 or x = 12
if x = 21
y = 40 – 21 = 19
Kamal's marks in mathematics and English are 21 and 19
if x = 12
y = 40 – 12 = 28
Kamal's marks in mathematics and English are 12 and 28