SOLUTION: What is the sum of the roots of the equation ax^2+bx+c=0

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Question 166538: What is the sum of the roots of the equation
ax^2+bx+c=0
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember the quadratic formula is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 note: a%3C%3E0


Now let w=sqrt%28+b%5E2-4ac+%29 (to simplify things a bit)


So the quadratic formula becomes


x+=+%28-b+%2B-+w%29%2F%282a%29


which really breaks down to


x+=+%28-b+%2B+w%29%2F%282a%29 or x+=+%28-b+-+w%29%2F%282a%29


So the first root is x%5B1%5D+=+%28-b+%2B+w%29%2F%282a%29 and the second root is x%5B2%5D+=+%28-b+-+w%29%2F%282a%29


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Adding the Roots:



x%5B1%5D%2Bx%5B2%5D Now let's add the roots


%28-b+%2B+w%29%2F%282a%29%2B%28-b+-+w%29%2F%282a%29 Plug in x%5B1%5D+=+%28-b+%2B+w%29%2F%282a%29 and x%5B2%5D+=+%28-b+-+w%29%2F%282a%29


%28-b+%2B+w-b+-+w%29%2F%282a%29 Combine the fractions.


%28%28-b-b%29+%2B+%28w-w%29%29%2F%282a%29 Group like terms.


%28-2b%29%2F%282a%29 Combine like terms. Notice how the "w" terms cancel each other out completely.


-b%2Fa Reduce


So this shows us that the sum of the roots of ax%5E2%2Bbx%2Bc is -b%2Fa


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What is the sum of the roots of the equation
ax^2+bx+c=0
Roots: x = [-b + sqrt(b^2-4ac)]2a or x = [-b -sqrt(b^2-4ac)]/2a
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Adding you get [-b/2a] + [-b/2a]
= 2[-b/2a]
= -b/a
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Cheers,
Stan H.