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anonymous
 one year ago
What are the possible numbers of positive, negative, and complex zeros of f(x) = −x^6 + x^5 − x^4 + 4x^3 − 12x^2 + 12?
Positive: 4, 2, or 0; negative: 2 or 0; complex: 6, 4, 2, or 0
Positive: 3 or 1; negative: 3 or 1; complex: 4, 2, or 0
Positive: 2 or 0; negative: 2 or 0; complex: 6, 4, or 2
Positive: 5, 3, or 1; negative: 1; complex: 4, 2, or 0
anonymous
 one year ago
What are the possible numbers of positive, negative, and complex zeros of f(x) = −x^6 + x^5 − x^4 + 4x^3 − 12x^2 + 12? Positive: 4, 2, or 0; negative: 2 or 0; complex: 6, 4, 2, or 0 Positive: 3 or 1; negative: 3 or 1; complex: 4, 2, or 0 Positive: 2 or 0; negative: 2 or 0; complex: 6, 4, or 2 Positive: 5, 3, or 1; negative: 1; complex: 4, 2, or 0

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know that you need to use the Descartes Rule or something like that, but I dont know how.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0yeah you look for changes of signs

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you help me find the answer?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0here's a good website http://www.purplemath.com/modules/drofsign.htm

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So 5 sign changes, now what can I do with that information?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1How many changes of signs do you see? dw:1443383107699:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Already posted it ;D

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1There maybe as many as 5 real roots. Since the polynomial has real coefficients, if it has complex roots, the complex roots must come in pairs of complex conjugate roots.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait never mind, Im guessing D.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1That means if it does have complex roots, it may have 2 (1 pair of complex conjugate roots) or 4 complex roots (2 pairs of complex conjugate roots).

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1That was the "positive:" case. Now replace x with x. (x) = −x^6  x^5 − x^4  4x^3 − 12x^2 + 12 Now there is only 1 sign change. There is only 1 negative root.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You are correct. D is the answer.
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