what two factors multiply to get -56 and add to get 20

Question

I need to know this answer (I can't seem to figure it out) and I need it for an assignment in math that is missing this is for 11 grade Math.

Answer 1

So..

a + b = 20

and

a * b = -56

If the product of the two factors is negative, you know that exactly one of the factors is negative.

To get this quickly, you solve one equation for b. Then you substitute that first equation into the other equation.

a + b = 20

becomes

b = 20 - a

Then substitute this into the second equation.

a * b = -56

a * (20 - a) = -56

20a - a^2 = -56

Then rearrange this last equation so that you can use the quadratic formula.

-a^2 + 20a + 56 = 0

You get...

10 + 2√(39)

and

10 - 2√(39)