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).
Step-by-step explanation:
Let [tex]x[/tex] and [tex]y[/tex] be the two numbers, the we know that
(1). [tex]xy=-12[/tex]
and
(2). [tex]x+y=-5[/tex]
We solve for [tex]y[/tex] in equation(2) and substitute this into equation(1)
[tex]y=-(5+x)[/tex]
[tex]xy=-x(x+5)=-12[/tex]
[tex]x^2+5x-12=0[/tex]
This is a quadratic equation, and its solutions are
[tex]x=1.772\\\\x=-6.772[/tex]
we substitute these two solutions into equation(1) and find the corresponding [tex]y[/tex] values:
[tex](1.772)y=-12\: \therefore y=-6.772[/tex]
[tex](-6.772)y=-12 \: \therefore y=1.772[/tex]
Thus we have two pairs of numbers which multiply to give -12 and add to give -5
[tex](1.772, -6.772)[/tex] and [tex](-6.772, 1.772).[/tex]
