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

Question

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

anonymous · Answer

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

anonymous · Answer

I prefer synthetic

anonymous · Answer

The polynomial is:
$$x^4 + 2x^2 - 80x - 75$$
right?

anonymous · Answer

Yes would I divide by -5. (synthetic)

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

yep, sure isn't a root

anonymous · Answer

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?

anonymous · Answer

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

anonymous · Answer

no they want the sum of the two other roots

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

yeah it's probably about 4, given the graph

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

you are welcome