SOLUTION: use a quadratic equation to find two real numbers that satisfy each equation. their sum is 12, and their product is -85

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: use a quadratic equation to find two real numbers that satisfy each equation. their sum is 12, and their product is -85      Log On


   

Question 1187927: use a quadratic equation to find two real numbers that satisfy each equation. their sum is 12, and their product is -85
Found 2 solutions by math_helper, Alan3354:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


x+y = 12    (1)

xy = -85    (2)





(1) -->  y = 12-x



Substitue this value of y into (2):  

x(12-x) = -85

+12x+-+x%5E2+=+-85+ 

+-x%5E2+%2B+12x+%2B+85+=+0+

+x%5E2+-12x+-85+=+0+



+%28x-17%29%28x%2B5%29+=+0+



x = 17 and  x = -5  satisfy this, and those are the two numbers.



Chack:

-5*17 = -85

and 

17+(-5) = 12

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
use a quadratic equation to find two real numbers that satisfy each equation. their sum is 12, and their product is -85
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There are not many pairs of integers with a product of 85.
----> -5 and 17
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Using a quadratic:
x*(12 - x) = -85
x^2 - 12x - 85 = 0
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Now to factor it, you have to find 5 and -17.
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If the solution was not 2 integers, the quadratic would be necessary.