Reprsent the following situations in the form of quadratic equations :

1.	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» 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.

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»

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.