What two numbers multiple to get -12 and add to -5

Question

asked Sep 22, 2021 175k views

1 Answer

Jason Axelson · Answer 1 · 2021-09-27T17:02:53+0000

Original question: What two numbers multiply to get -12 and add to -5.

Answer:

Pairs of numbers (1.772, -6.772) and (-6.772, 1.772).

Explanation:

Let
and
be the two numbers, the we know that

(1).
xy=-12

and

(2).
x+y=-5

We solve for
in equation(2) and substitute this into equation(1)

y=-(5+x)

xy=-x(x+5)=-12

x^2+5x-12=0

This is a quadratic equation, and its solutions are

$x=1.772\\\\x=-6.772$

we substitute these two solutions into equation(1) and find the corresponding
values:

$(1.772)y=-12\: \therefore y=-6.772$

$(-6.772)y=-12 \: \therefore y=1.772$

Thus we have two pairs of numbers which multiply to give -12 and add to give -5

(1.772, -6.772) and
(-6.772, 1.772).