SOLUTION: the sum of two numbers is 9 and their product is 20. use a quadratic equation to determine the two numbers

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Question 521728: the sum of two numbers is 9 and their product is 20. use a quadratic equation to determine the two numbers

Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be A and B. Then...
A%2BB+=+9 and...
A%2AB+=+20
Rewrite the first equation as:
A+=+9-B and substitute for a in the second equation.
%289-B%29%2AB+=+20 Simplify.
9B-B%5E2+=+20 Rewrite as a quadratic equation in standard form.
-B%5E2%2B9B-20+=+0 Apply the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a (x is really B, one of the two numbers). In this problem, from the quadratic equation, a = -1, b = 9, and c = -20.
B+=+%28-9%2B-sqrt%289%5E2-4%28-1%29%28-20%29%29%29%2F2%28-1%29
B+=+4.5%2B%28-0.5%29 or B+=+4.5-%28-0.5%29
B+=+4 or B+=+5
The two numbers are 4 and 5.