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

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) (Show Source): You can put this solution on YOUR website!
Remember the quadratic formula is:

note:

Now let (to simplify things a bit)

So the quadratic formula becomes

which really breaks down to

or

So the first root is and the second root is

==========================================

Adding the Roots:

Now let's add the roots

Plug in and

Combine the fractions.

Group like terms.

Combine like terms. Notice how the "w" terms cancel each other out completely.

Reduce

So this shows us that the sum of the roots of is

Answer by stanbon(75887) (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
---------------
Adding you get [-b/2a] + [-b/2a]
= 2[-b/2a]
= -b/a
===============
Cheers,
Stan H.
RELATED QUESTIONS
what is the sum of the roots of the equation ax exponent 2+bx+c=0? (answered by Earlsdon)
What is the sum of the roots of the equation ax^2 + bx + c... (answered by htmentor)
What is the sum of the roots of the equation ax(squared) +bx +c... (answered by Alan3354)
what is the sum of roots of... (answered by jim_thompson5910)
what is the sum of the roots of the quadratic equation: ax^2 + bx + c = 0, where a, b,... (answered by Fombitz)
i am asked what are the sum of the roots of the equation ax^2+bx+c=0 is the answer1 i... (answered by jsmallt9)
what is the sum of the roots of this equation. ax^2+bx+c=0 im not sure what they mean by... (answered by josmiceli)
prove that if the sum of the sequence of the roots of the equation ax^2+bx+c=0 is 1 then... (answered by math_tutor2020)
prove that if the sum of the sequence of the roots of the equation ax^2+bx+c=0 is 1 then... (answered by ikleyn)