SOLUTION: Find the two numbers whose sum is 50 and whose product is 621.

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Question 223934: Find the two numbers whose sum is 50 and whose product is 621.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
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 -x%5E2%2B50x-621=0 or x%5E2-50x%2B621=0

Step 4. To solve, use quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=-50, and c=621

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-50x%2B621+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-50%29%5E2-4%2A1%2A621=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--50%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-50%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+27
x%5B2%5D+=+%28-%28-50%29-sqrt%28+16+%29%29%2F2%5C1+=+23

Quadratic expression 1x%5E2%2B-50x%2B621 can be factored:
1x%5E2%2B-50x%2B621+=+1%28x-27%29%2A%28x-23%29
Again, the answer is: 27, 23. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-50%2Ax%2B621+%29



(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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Good luck in your studies!

Respectfully,
Dr J