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LilyMQ
 one year ago
What are the possible number of positive, negative, and complex zeros of f(x) = x^6  x^5 x^4  4x^3  12x^2 + 12
LilyMQ
 one year ago
What are the possible number of positive, negative, and complex zeros of f(x) = x^6  x^5 x^4  4x^3  12x^2 + 12

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LilyMQ
 one year ago
Best ResponseYou've already chosen the best response.0The options are 1. Positive: 4, 2, or 0; Negative: 2 or 0; Complex: 6, 4, 2, or 0 2. Positive: 3 or 1; Negative: 3 or 1; Complex: 4, 2, or 0 3. Positive: 3 or 1; Negative: 2 or 0; Complex: 4, 2, or 0 4. Positive: 1; Negative: 5, 3, or 1; Complex: 4, 2, or 0

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Let P = max number of positive zeros, N = max number of negative zeros and n  (P+N) the minimum number of complex. n is the degree of the polynomial n=6 Signs of coefs from highest to lowest: {,,,,,0,+}. Positive zeros (P) : Number of sign changes: 1 Now negate the odd terms: {,+,,+,,0,+} Negative zeros (N): Number of sign changes: 5,3,1 Complex zeros (min): 6  (1+5) = 0 6  (1+3) = 2 6  (1+1) = 4 $$ \href{https:///en.wikipedia.org/wiki/Descartes%27_rule_of_signs}{\text{Descarte's Rule}} $$ Does this make sense?
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