Question

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

Answer 1

ANSWER :

QUADRATIC EQUATION :

• If p ( x ) is a quadratic equation, then p(x) = 0 is called a Quadratic Equation.

• The general formula of a Quadratic Equation :

         ax² + bx + c = 0.

WHAT IS AN INTEGERS ?

• An integers are those numbers which cannot be written in fractions. ( not a fractional numbers...)

• A whole number , anywhere from zero to positive ( + ) and negative ( - ) infinity are integers.

• Examples : -3. -2 , -1 , 1 , 2 , 3 etc...

Consecutive Positive Integers :

• x, x + 1, x + 2 are three Consecutive Positive Integers.

→

Let the two consecutive integers be x , ( x + 1 ) ,According to given question we have :

The product of two consecutive positive integers = 306 ( given )

→ x ( x + 1 ) = 306

→ x² + x = 306

→ x² + x - 306 = 0

• FINAL ANSWER :

x² + x - 306 = 0 , WHERE " x " IS THE SMALLER INTEGER.

SOLVING THIS QUADRATIC EQUATION NOW :

( By the splitting the middle term method...)

→ x² + x - 306 = 0

→ x² + 18x - 17x - 306 = 0

→ x(x + 18) - 17(x + 18) = 0

→  (x + 18)(x - 17) = 0

(x + 18) = 0    ,     (x - 17) = 0

∴ x = ₋ 18      ,     ∴ x =  17

x = 17  

When x = 17,

x + 1 = 17 + 1

→ 18

⇒  Hence, the integers are 17 and 18.

Answer 2

Refers to attachment ✔✔