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

Answer 1

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

Answer 2

I prefer synthetic

Answer 3

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

Answer 4

Yes would I divide by -5. (synthetic)

Answer 5

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

Answer 6

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

Answer 7

yep, sure isn't a root

Answer 8

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?

Answer 9

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

Answer 10

no they want the sum of the two other roots

Answer 11

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

Answer 12

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

Answer 13

yeah it's probably about 4, given the graph

Answer 14

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

Answer 15

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

Answer 16

you are welcome