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what are the number of variations in your positive setup?
I was thinking that it was 3 variations
2x^4 -7x^3 +3x^2 +8x -4 | | | 0 1 2 3 i count 3 as well
do you recall that a root can be repeated right?
I was thinking about that also, but why would we have to subtract the number of variations by 2, instead of 1, if we were accounting for repeats?
the subtraction by 2 is to account for complex (nonreal) roots which always come in conjugate pairs
I see. What would we do about the repeating roots, then?
repeating roots was just a thought, but it has 3 postivie roots http://www.wolframalpha.com/input/?i=0%3D2x^4-7x^3%2B3x^2%2B8x-4
does the question ask you to find the roots? or just the number of them?
It asks to find all the real roots.
and you are sure that your looking up the right answer key with the right question? also, books do have errors in them
attaching a picture might help verify your cause :)
Yep, it has the roots 1/2, 2, and -1. Doesn't the graph in the link have two positive roots and one negative root? :o
i am so glad you are on top of these things ... so yeah, there is a double root. so, it has 3 positive roots. 1/2, 2, 2 it is just that one of them occurs more than once.
Okays, so when solving these kinds of problems, we should assume there is a double root if the answer isn't the correct number of variations?
you discover it either by working out the division ... or by the graph
I see. Graphing...
as long as no errors occur in print, yeah, you can assume that one or more of the roots are a multiple root if we count 3 or 1, and only find '2' of them.