Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 7 of Exercise 10E
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The product of two consecutive positive integers is 306. Find the integers.
Let the two consecutive positive integers be x and (x + 1)
According to given condition,
x(x + 1) = 306
x2 + x – 306 = 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 = 1 c = – 306
= 1. – 306 = – 306
And either of their sum or difference = b
= 1
Thus the two terms are 18 and – 17
Difference = 18 – 17 = 1
Product = 18. – 17 = – 306
x2 + x – 306 = 0
x2 + 18x – 17x – 306 = 0
x(x + 18) – 17(x + 18) = 0
(x + 18) (x – 17) = 0
(x + 18) = 0 or (x – 17) = 0
x = – 18 or x = 17
but x = 17 ( x is a positive integers)
x + 1 = 17 + 1 = 18
Thus the two consecutive positive integers are 17 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.