Question

The product of two consecutive integers is 240. The quadratic representation of the above situation is

x2+(x+1)=240
x(x+1)=240
5x2+8x+4=2x2+4x+6
x(x+1)2=240

Answer 1

Answer:

x(x+1)=240

Step-by-step explanation:

The product of two consecutive integers is 240

The product of x  and x+1 is x*(x+1)

Equation: x*(x+1)=240

-------------------

x2+(x+1)=240  - incorrect

x(x+1)=240 - correct

5x2+8x+4=2x2+4x+6  -incorrect

x(x+1)2=240 - incorrect

Answer 2

$\sf\huge\bold{Answer:}$

Given :

The product of two consecutive integers is 240.

To find :

Correct relation according to statement.

Solution :

• Consecutive numbers

Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number.

Example : 1 and 2, 7 and 8

Let the first number be x

So, the next consecutive number will be (x+1)

Now, it is given that their product will be 240.

According to question :

→x(x+1)=240

Equation formed is x(x+1)=240

Now, let us find the consecutive numbers

Solving the equation formed

→x(x+1)=240

→x²+x=240

→x²+x-240=0

• General form of Quadratic equation :

ax²+bx+c=0

• On comparing, we get

a= 1

b=1

c= -240

• Discriminant

D=b²-4ac

D=1²-4(1)(-240)

D=1-(-240)

D=1+240

D=241

• Roots

→x= -b±√D/2a

→x= -1±√241/2(1)

→x= -1±√241/2

Hence, the two numbers will be x= -1±√241/2

i.e x= -1+√241/2 & x= -1-√241/2