The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring

Question

asked Oct 21, 2020 117k views

2 Answers

Hertzel Guinness · Answer 1 · 2020-10-26T06:16:15+0000

For this case we have
20 * 21 = 420. We must find an equation that allows us to find the smallest value. So:

Let "x" be the variable that represents the smallest number. Thus, "x + 1" represents the consecutive integer. The equation would be given by:

$x * (x + 1) = 420\\x ^ 2 + x = 420\\x ^ 2 + x-420 = 0$

To factor, we must find two numbers that multiply as a result -420 and sum as a result 1.

These numbers are:

$21, -20\\21-20 = 1\\21 * (-20) = -420$

Thus, the factorization is:

(x-20) (x + 21) = 0

The roots are:

$x = 20\\x = -21$

Effectively, the smallest integer was found,
x = 20 .

Answeer:

$x ^ 2 + x-420 = 0\\(x-20) (x + 21) = 0$