Question

The product of two consecutive positive integers is 306 we need to Find the integers. Form Quadratic equation

Answer 1

Answer:

The quadratic equation is $x^2+x-306=0$ and the integers are 17 and 18.

Step-by-step explanation:

Take the consecutive positive integers to be $x$ and $x+1$.

Given that the product of these numbers is 306.

We can formulate the quadratic equation,

$\implies x(x+1)=306\\\\\implies x^2+x=306\\\\\implies x^2+x-306=0$

This is the required quadratic equation.

We can solve the equation to find those positive integers.  

Factorizing the quadratic equation, we obtain

$x^2+x-306 =(x-17)(x+18)$

So the solutions of the equation are 17 and -18. Since the numbers are positive integers we can take the value of $x$ to be 17.

So the integers are 17 and 18.

Answer 2

Answer:

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.