Answer:
The quadratic equation is x² + x - 420 = 0 and value of x is 20.
Step-by-step explanation:
As given
The product of two consecutive integers is 420.
As the one consecutive number be x.
The other consecutive number be x + 1.
Than the equation becomes
x (x + 1 ) = 420
x² + x = 420
x² + x -420 = 0
x² + 21x - 20x - 420 = 0
x (x + 21) - 20 (x + 21) = 0
(x - 20) (x + 21) = 0
As x = 20 and x = - 21
The value x = -21 (Neglected because x + 1 = -21 +1 = -20 , becomes smaller value.)
Than
x = 20
Than
(x + 1)= 20 + 1
= 21
Therefore the value of x is 20 .
