Question

The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if x denotes the smaller integer.

Answer 1

SOLUTION :  

Given : The product of two consecutive positive integers is 306.

Let two consecutive positive integers are x and (x + 1)  

A.T.Q  

Product of x and (x + 1) = 306  

x(x + 1) = 306  

x² + x = 306

x² + x - 306 = 0

Hence, x² + x - 306 = 0 is the required quadratic equation.

By factorisation,  

x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0

⇒ x = 17 and -18

But x ≠ -18 because x is a  positive integer.

Therefore, x = 17

One positive integer (x) = 17

Other positive integer = x +1 = 17 + 1= 18  

Hence, the two consecutive positive integers are 17 and 18 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

According to the question, the smaller of the given two positive integers is denoted by ' x '.

Since, the two positive integers are consecutive, the other positive integer will be, " ( x + 1 ) ".


Again according to the question,
( x ) * ( x + 1 ) = 306
=> x² + x = 306
=> x² + x - 306 = 0
The required quadratic equation = x² + x - 306 = 0

We have already found the quadratic equation, so why not calculate further?

x² + x - 306 = 0
x² + 17x - 18x - 306 = 0
x ( x + 17 ) - 18 ( x + 17 ) = 0
( x + 17 ) ( x - 18 ) = 0

By zero product rule,

x = - 17 OR x = 18

It is provided in the question that ' x ' necessarily be a positive integer do we are taking the positive value of ' x '.

Hence,

First consecutive integer = x = 18
Second positive integer = x + 1 = 18 + 1 = 19