Question

What two numbers = -48 (multiply) and does the two numbers = -13

Answer 1

Answer:

The two numbers are $3$ and $-16$.

Step-by-step explanation:

Two numbers that, when multiplied, result in a product of $-48$:

$x \cdot y = -48$

Same two numbers when added get a sum of $-13$:

$x + y = -13$

Solve for x in the summation identity:

$y = -13 - x$

Plug the value back into the product identity and solve for $x$:

$x \cdot (-13-x) = -48\\-13x - x^2 = - 48\\x^2 + 13x = 48\\x^2 + 13x - 48 = 0\\(x-3)(x+16) = 0$

The roots we found for $x$ were:

$x = 3\\x = -16$

Our two numbers are $3$ and $-16$. We can test this:

$3 + (-16) = -13\\3 * -16 = -48$