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

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

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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