What two number multiply to - 21 and add to 20

-1 and 21

Step-by-step explanation:

Let the numbers be x and y.

x + y = 20

xy = - 21

Solve the first equation for x and substitute in the second equation.

x = 20 - y

(20 - y) y = - 21

20y - y^2 = - 21

y^2 - 20y - 21 = 0

(y - 21) (y + 1) = 0

y - 21 = 0 or y + 1 = 0

y = 21 or y = - 1

For y = 21:

x = 20 - y

x = 20 - 21

x = - 1

For y = - 1:

x = 20 - y

x = 20 - (-1)

x = 21

Solutions: (-1, 21) and (21, - 1)

Answer: the numbers are - 1 and 21

21 * (-1) = - 21

21 + (-1) = 20