what two numbers add up to -23 and multiply to make 120?

• (-8) + (-15) = -23

and

(-8) (-15) = +120

1) Form equations and solve to get the answer.

Here, the eqns are x + y = -23 and xy = 120

y = -23 -x

Sub in the other as x(-23-x) = 120

-23x-x^2 = 120

x^2 + 23x + 120 = 0

Solution for this is

x = [ -23 + sqrt{23^2 - 4(1)(120)} ]/2 and

x = [ -23 - sqrt{23^2 - 4(1)(120)} ]/2

Solve and u'll get -8 and -15

2) Trial & Error

120 = 12 * 10

= 4 3 5 * 2

= 4 ( 3 5) * 2 ---> Combine suct that their sum is 23.

= (42) (35)

= 8 * 15 --->8+15=23

Since the req. 2 nos. add to give -23, ur answer should be negative.

Therefore, -8 and -15

It is known that multiplication of 2 negative nos. yields a positive number.

• Many of these types of problems are trial and error.

First, what two numbers add up to -23 that are fairly big numbers (since they have to make a large number: 120).

After trial and error, I figured out it is -8 and -15.

Hope that helps!

• x + y = -23

xy = 120

x( -23 - x) = 120

-23x - x^2 = 120

0 = x^2 + 23x + 120

0 = (x + 15)(x + 8)

x = -15 or x = -8

• x+y=-23 ==> y=-x-23

xy=120

x(-x-23)=120

x^2+23x+120=0

[-23+/- sqrt(23^2-4(1)(120))]/2

x = -15, y = -8

• What Two Numbers

• X + Y = -23

X times Y = 120

Use this system of equation to solve.

you will get -15 and -8

• -8 and -15

• -15 and -8

• x= first number

y= second number

1st equation x+ y = -23 or y= -23-x

2nd equation x*y= 120

Substituting 1 in 2

.... x times (-23-x)= 120

Now please solve the quadratic equation and find the x. If nobody does iyt for you and you cant e-maill me

• x+y=-23

x=-23-y

Also

xy=120

so substitute the -23-y for x and you get

y(-23-y) =120

y^2-23y=120