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Find the two numbers whose sum is 50 and whose product is 621.
Step 1. Let x be one number.
Step 2. Let 50-x be the other number since the sum is 50.
Step 3. Then, x(50-x)=621 or
Step 4. To solve, use quadratic formula given as
where a=1, b=-50, and c=621
|Solved by pluggable solver: SOLVE quadratic equation with variable|
|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=16 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 27, 23.
Here's your graph:
(please ignore the graph since it's the numbers are out of scale)
Step 5. ANSWER: The numbers are 23 and 27.
I hope the above steps were helpful.
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