Question

What multiplies to -100 and adds to 0

Answer 1

To find two numbers that multiply to -100 and add to 0, you can set up the equations:

1. \( x \cdot y = -100 \)
2. \( x + y = 0 \)

From the second equation, \( y = -x \). Now, substitute \( y \) in the first equation:

\[
x \cdot (-x) = -100
\]

This simplifies to:

\[
-x^2 = -100
\]

And then:

\[
x^2 = 100
\]

Taking the square root gives:

\[
x = 10 \quad \text{or} \quad x = -10
\]

Thus, the two numbers are \( 10 \) and \( -10 \).

To verify:

- \( 10 \cdot (-10) = -100 \)
- \( 10 + (-10) = 0 \)

So, the two numbers that multiply to -100 and add to 0 are \( 10 \) and \( -10 \).