SOLUTION: use a quadratic equation to find two real numbers that satisfy each situation, or show that no such numbers exist their sum is 12, and their product is20

Question 677089: use a quadratic equation to find two real numbers that satisfy each situation, or show that no such numbers exist
their sum is 12, and their product is20
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
show that no such numbers exist
their sum is 12, and their product is 20
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Equations:
x + y = 12
xy = 20
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Substitute for "x" and try to solve:
(12-y)y = 20
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12y - y^2 = 20
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y^2 - 12y + 20 = 0
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y = [12 +- sqrt(144-4*20)]/2
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y = [12 +- sqrt(64)]/2
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y = [12+-8]/2
y = 10 or y = 2
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If y = 10, x = 2
If y = 2, y = 2
====================
The numbers DO exist.
====================
Cheers,
Stan H.
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