what two numbers add up to -23 and multiply to make 120?
What are two numbers that add up to -23 and multiply to 120?
10 Answers
x+y=-23 ==> y=-x-23
xy=120
x(-x-23)=120
x^2+23x+120=0
Solve for quadratic equation:
[-23+/- sqrt(23^2-4(1)(120))]/2
x = -15, y = -8
X + Y = -23
X times Y = 120
Use this system of equation to solve.
you will get -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
Then use the quadratic formula.
x is plus or minus 11.5,
(-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!
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