The product of two consecutive positive integers is 306. We need to find the integers.

Question

Reprsent the following situations in the form of quadratic equations :

The product of two consecutive positive integers is 306. We need to find the integers.

Answer 1

Let one positive integer be x’. 

The Next integer is (x + 1) 

Their product is 306. 

∴ x (x + 1) = 306 

x² + x = 306 

∴ x² + x – 306= 0. 

This is required equation. 

Now, we have to solve for positive integer. 

x² + x – 306 = 0 

x² + 18x – 17x – 306 = 0 

x(x + 18) – 17(x + 18) = 0 

(x + 18) (x – 17) = 0 

If x + 18 = 0, then x = -18 

If x – 17 = 0, then x = 17 

∴ x = 18, OR x = 17.