Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 11 of Exercise 10E
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Find two consecutive positive even integers whose product is 288.
Let the two consecutive positive even integers be x and (x + 2)
According to given condition,
x (x + 2) = 288
x2 + 2x – 288 = 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 = 2 c = – 288
= 1. – 288 = – 288
And either of their sum or difference = b
= 2
Thus the two terms are 18 and – 16
Difference = 18 – 16 = 2
Product = 18. – 16 = – 288
x2 + 18x – 16x – 288 = 0
x (x + 18) – 16(x + 18) = 0
(x + 18) (x – 16) = 0
(x + 18) = 0 or (x – 16) = 0
x = – 18 or x = 16
x = 16 (x is a positive odd integer)
x + 2 = 16 + 2 = 18
Hence, the required integers are 16 and 18
minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.
