anonymous
  • anonymous
What are the possible number of positive, negative, and complex zeros of f(x) = -3x4 - 5x3 - x2 - 8x + 4 ? A) Positive: 2 or 0; Negative: 2 or 0; Complex: 4 or 2 or 0 B) Positive: 1; Negative: 3 or 1; Complex: 2 or 0 C) Positive: 3 or 1; Negative: 1; Complex: 2 or 0 D) Positive: 4 or 2 or 0; Negative: 2 or 0; Complex: 4 or 2 or 0
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
the numbers after the x's are exponents, correct?
anonymous
  • anonymous
yes
anonymous
  • anonymous
there are 2 positive and 2 complex roots

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anonymous
  • anonymous
i've tried using descartes rule of signs but i got confused to be honest so i solved it
anonymous
  • anonymous
one root lie b/w 0 and 1
anonymous
  • anonymous
right
anonymous
  • anonymous
other will be negative as f(x) is increasing in R+
anonymous
  • anonymous
Am i right????
anonymous
  • anonymous
no 2 positive
anonymous
  • anonymous
yeah 1 will be positive and one will not be possitive it can also be possilbe that roots may be irrational becuase irrational roots also exist in pairs
anonymous
  • anonymous
there is 1 sign change so by DRS there is 1 positive root Sub -x for x to get negative roots, 3 sign changes so 3 or 1 negative roots Complex roots are total roots, 4, less positive and negative roots so 0 or 2 of those. Answer is B

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