Questions on Algebra: Linear Algebra (NOT Linear Equations) answered by real tutors!

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

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.