Question

Represent the following situation in the form of quadratic equations :
The product of two consecutive positive integers is 306. We need to find the integers.

Answer 1

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

a/c to question, The product of two consecutive positive integers is 306.
e.g., x × (x + 1) = 306

=> x² + x - 306 = 0

hence, x² + x - 306 = 0 is the form of quadratic equation.

now, x² + x - 306 = 0

=> x² + 18x - 17x - 306 = 0

=> x(x + 18) - 17(x + 18) = 0

=> (x - 17)(x + 18) = 0

=> x = -18 and 17 but x ≠ -18 because x is positive integer.

so, x = 17 and x + 1 = 18
therefore, two positive integers are 17 and 18

Answer 2

SOLUTION :

Given : The product of two consecutive positive integers is 306

Let two consecutive positive integers be x and (x + 1) .  

A.T.Q

x × (x + 1) = 306  

x² + x = 306  

x² + x - 306 = 0

which is the required QUADRATIC EQUATION.

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

x² + x - 306 = 0

x² + 18x - 17x - 306 = 0

[By factorization]

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

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

(x - 17)= 0 or (x + 18) = 0

x = 17 or x = -18  

[x can't be negative because x is positive integer]

so, x = 17  

First positive Integer = x = 17  

Second positive Integer = x + 1 = 17 +1= 18  

Hence, the two positive integers are 17 and 18.

HOPE THIS ANSWER WILL HELP YOU...