Question

What multiplies to -5 and adds to 4

Answer 1

To find two numbers that multiply to -5 and add up to 4, we can set up the following system:

Let the two numbers be \( x \) and \( y \).

1. \( x \cdot y = -5 \)
2. \( x + y = 4 \)

We can express \( y \) in terms of \( x \) using the second equation:

\[
y = 4 - x
\]

Now, substitute this expression for \( y \) into the first equation:

\[
x(4 - x) = -5
\]

Expanding this gives:

\[
4x - x^2 = -5
\]

Rearranging it into standard quadratic form:

\[
x^2 - 4x - 5 = 0
\]

Now we can factor the quadratic:

\[
(x - 5)(x + 1) = 0
\]

Setting each factor to zero gives us:

\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]

So the two numbers are \( x = 5 \) and \( y = -1 \) (or vice versa).

**Answer:** 5 and -1 (or -1 and 5)