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
so we can use division to factor out the two roots we are given
I prefer synthetic
The polynomial is: \[x^4 + 2x^2 - 80x - 75\] right?
Yes would I divide by -5. (synthetic)
you would, but you find that -5 isn't a root of the polynomial at all
in fact, just to check, I looked here: http://www.wolframalpha.com/input/?i=factor+x%5E4+%2B+2x%5E2++-+80x+-75
yep, sure isn't a root
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?
well, fist of all, none of them will come out to be 0
no they want the sum of the two other roots
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
in fact, unless either a or b is 0, in a quadratic a+b will NEVER be a root.
yeah it's probably about 4, given the graph
seems like the closest one to the sum of the real roots
Yeah, I took a look at the graph and guessed 4. Thank you for the input guys.
you are welcome
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