SOLUTION: find two numbers whose sum is 55 and whose product is 684

Question 162375: find two numbers whose sum is 55 and whose product is 684

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
find two numbers whose sum is 55 and whose product is 684
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Call the numbers x and y.
x+y = 55
xy = 684
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From the 1st eqn, y = 55-x
Sub that into the 2nd eqn
x*(55-x) = 684
55x - x^2 = 684
x^2 - 55x + 684 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=289 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 36, 19. Here's your graph:

The graph isn't much help, but the numbers are given:
19 and 36

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