SOLUTION: what is the sum of the roots of the quadratic equation: ax^2 + bx + c = 0, where a, b, and c are all non-zero real constants

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: what is the sum of the roots of the quadratic equation: ax^2 + bx + c = 0, where a, b, and c are all non-zero real constants      Log On

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Question 108591: what is the sum of the roots of the quadratic equation: ax^2 + bx + c = 0, where a, b, and c are all non-zero real constants
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
This is the general form of a quadratic equation.
It's solution are given by the quadratic formula.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
One solution, x%5B1%5D, adds that expression under the square root symbol, let's call that R.
x%5B1%5D=%28-b+%2B+R%29%2F%282%2Aa%29+
The other solution, x%5B2%5D, subtracts it.
x%5B2%5D=%28-b+-+R%29%2F%282%2Aa%29+
When you add them together they cancel out and you are left with.
x%5B1%5D%2Bx%5B2%5D=%28-b%2BR%29%2F%282%2Aa%29%2B%28-b-R%29%2F%282%2Aa%29+
x%5B1%5D%2Bx%5B2%5D=%28%28-b%2BR%29%2B%28-b-R%29%29%2F%282%2Aa%29
x%5B1%5D%2Bx%5B2%5D=%28-b%2BR-b-R%29%2F%282%2Aa%29
x%5B1%5D%2Bx%5B2%5D=%28-2%2Ab%29%2F%282%2Aa%29
x%5B1%5D%2Bx%5B2%5D=%28-b%29%2Fa