Question

Two numbers multiply together to give -20 and add together to give -1.

What are the two numbers?

Answer 1

[AI-generated answer — Bot]

The two numbers are -5 and 4.

Explanation:

To find two numbers that multiply to give -20, we need to consider all the possible pairs of factors of 20. These are:

1, 20
2, 10
4, 5

Since the product of the two numbers is negative, one of the numbers must be negative and the other positive. In addition, we know that their sum is -1, so the negative number must be greater in absolute value than the positive number.

The only pair of numbers that satisfies these conditions is -5 and 4.

-5 * 4 = -20
-5 + 4 = -1

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the two numbers, let's assume that the two numbers are x and y.

Given that the two numbers multiply together to give -20, we can write the equation as:

x * y = -20 --(Equation 1)

Also, given that the two numbers add together to give -1, we can write the equation as:

x + y = -1 --(Equation 2)

Now, we can solve these two equations simultaneously to find the values of x and y.

Let's solve Equation 2 for x:

x = -1 - y --(Equation 3)

Substitute Equation 3 into Equation 1:

(-1 - y) * y = -20

Multiply out the terms:

-y^2 - y = -20

Rearrange the equation:

y^2 + y - 20 = 0

Now, we can solve this quadratic equation to find the possible values of y.

Factoring the equation, we have:

(y + 5) * (y - 4) = 0

Setting each factor equal to zero, we get:

y + 5 = 0 --> y = -5

or

y - 4 = 0 --> y = 4

So, the possible values of y are -5 and 4.

Now, substitute these values of y back into Equation 2 to find the corresponding values of x.

For y = -5:

x + (-5) = -1
x - 5 = -1
x = 4

For y = 4:

x + 4 = -1
x = -5

Therefore, the two numbers are -5 and 4.