Question

The product of two consecutive room numbers is 420. find the room numbers.

Answer 1

Hello : 
the  consecutive room numbers are : n , n+1
n(n+1) =420
n²+n -420 = 0 
the discriminant delta = b² - 4ac       ( a = 1  and b =  1  and   c = - 420
delta = (1)²-4(1)(-420) =1681= 41²
n = (-1 -41)/2    ( refused negatif number)
or 
n = (-1+41)/2 =20
 the room numbers.are : 20  , 21

Answer 2

Step-by-step explanation:

Let the first number is x and other number is (x+1). The product of two consecutive room numbers is 420.

So, according to question,

$x\times (x+1)=420$

$x^2+x-420=0$

On solving the above quadratic equation, we get the value of x as:

x = 20

and

(x+1) = 21

So, two numbers are 20 and 21.