Question

The product of two consecutive integers is $420$. Find the integers.

Short answer

The integers are$20,21and-20,-21.$

Step-by-step solution

Step 1. Given Information.

The product of two consecutive integers are $420.$

Step 2. Factor the Equation

According to the question,

$$\begin{gathered} x(x+1)=420 \\ {x}^2+x-420=0 \\ {x}^2+21x-20x-420=0 \\ x(x+21)-20(x+21)=0 \\ (x-20)(x+21)=0 \end{gathered}$$

Step 3. Solution of the equation.

Using the Zero Product property,

$$\begin{gathered} x-20=0 \\ x=20 \\ x+1=21 \\ Also, \\ x+21=0 \\ x=-21 \\ x+1=-20 \end{gathered}$$