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anonymous
 one year ago
Descartes' Rule of Signs: 2x^47x^3+3x^2+8x4
This equation shows that there would be either 3 positive roots, or 1 positive root, but my answer and the answer at the back of my textbook say that there are only two positive roots; 1/2, and 2.
The Descartes' Rule of Signs says that the number of positive roots is either equal to the number of variations in sign or is less than that by an even whole number. Why does that not apply to this equation?
anonymous
 one year ago
Descartes' Rule of Signs: 2x^47x^3+3x^2+8x4 This equation shows that there would be either 3 positive roots, or 1 positive root, but my answer and the answer at the back of my textbook say that there are only two positive roots; 1/2, and 2. The Descartes' Rule of Signs says that the number of positive roots is either equal to the number of variations in sign or is less than that by an even whole number. Why does that not apply to this equation?

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amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what are the number of variations in your positive setup?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I was thinking that it was 3 variations

amistre64
 one year ago
Best ResponseYou've already chosen the best response.12x^4 7x^3 +3x^2 +8x 4    0 1 2 3 i count 3 as well

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1do you recall that a root can be repeated right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1the subtraction by 2 is to account for complex (nonreal) roots which always come in conjugate pairs

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I see. What would we do about the repeating roots, then?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1repeating roots was just a thought, but it has 3 postivie roots http://www.wolframalpha.com/input/?i=0%3D2x^47x^3%2B3x^2%2B8x4

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1does the question ask you to find the roots? or just the number of them?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It asks to find all the real roots.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1and you are sure that your looking up the right answer key with the right question? also, books do have errors in them

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1attaching a picture might help verify your cause :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep, 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

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1i 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okays, 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?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1you discover it either by working out the division ... or by the graph

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1as 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.
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