Question

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

Answer 1

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

solution :

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…

 

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Answer 2

Step-by-step explanation:

Hi ,

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

integers ,

x( x + 1 ) = 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 is a positive integer,