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Mathematics 72 Online
OpenStudy (anonymous):

Given that -5 is a double root of x4 + 2x2 - 80x-75= 0, find the sum of the remaining roots A) 2 B) 4 C) -2 D) -4

OpenStudy (anonymous):

so we can use division to factor out the two roots we are given

OpenStudy (anonymous):

I prefer synthetic

OpenStudy (anonymous):

The polynomial is: \[x^4 + 2x^2 - 80x - 75\] right?

OpenStudy (anonymous):

Yes would I divide by -5. (synthetic)

OpenStudy (anonymous):

you would, but you find that -5 isn't a root of the polynomial at all

OpenStudy (anonymous):

in fact, just to check, I looked here: http://www.wolframalpha.com/input/?i=factor+x%5E4+%2B+2x%5E2++-+80x+-75

OpenStudy (anonymous):

yep, sure isn't a root

OpenStudy (anonymous):

Making a wild guess I think it might be 4. I'm not sure though. Question said that -5 is the double root of the equation listed. Could I just plug in each number into x to see which one comes out to zero?

OpenStudy (anonymous):

well, fist of all, none of them will come out to be 0

OpenStudy (anonymous):

no they want the sum of the two other roots

OpenStudy (anonymous):

and, no you can't, because a being a root and b being a root doesn't necessarily mean that a+b is a root

OpenStudy (anonymous):

in fact, unless either a or b is 0, in a quadratic a+b will NEVER be a root.

OpenStudy (anonymous):

yeah it's probably about 4, given the graph

OpenStudy (anonymous):

seems like the closest one to the sum of the real roots

OpenStudy (anonymous):

Yeah, I took a look at the graph and guessed 4. Thank you for the input guys.

OpenStudy (anonymous):

you are welcome

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