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What I want to do in this video is find out if there is any fast way

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to figure out the sum of the roots of any polynomial

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And there actually is and that's why I'm doing this video

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So lets start with a second degree polynomial

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so lets say it's x squared plus a one x plus a two is equal to zero

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so this is just a standard quadratic equation right here, second degree equation

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and you might be saying hey but you put the coefficent

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on the x term equal to one

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and in general you can always convert any polynomial

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and I'll do it with a second degree but if you have

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A x squared plus B x plus C is equal to 0

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then you can just divide both sides of this equation by A

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and you're going to have something that's in this form

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where the coefficent on the x squared term

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is going to be equal to one.

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And you can do that with any polynomial that's set equal to 0

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so with that out of the way let's think about what the

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sum of the roots of this are going to be

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so this is a second degree polynomial

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it's a quadratic equation, so it'll have two roots

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they can be real or complex

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so let's call the roots R one and R two

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and that tells us that these are roots that

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X minus R 1 times X minus R 2

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is going to be equal to 0

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and if we multiply this out we get

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X times X is X squared

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X times negative R2 is negative R2X

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and then we have negative R1 times X and negative R1X

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and then we have negative R1 times negative R2

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which is plus R1R2 is equal to 0

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and we can simplify this middle term a little bit

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it becomes x squared minus R1 plus R2