anonymous
  • anonymous
1
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
and the rational zeros theroem
anonymous
  • anonymous
if you just want to know the possible combinations of positive/negative/complex solutions, use descartes rule of signs by itself
anonymous
  • anonymous
so that means there are either 3 positive real zeros or 1 positive real zero

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anonymous
  • anonymous
you must analyze f(-x) for possible negative real zeros
anonymous
  • anonymous
no, plug in -x for x
anonymous
  • anonymous
f(x) = 7x^5 + 15x^4 – x^3 + 4x^2 – 6x – 11 f(-x)=7(-x)^5+15(-x)^4-(-x)^3+4(-x)^2-6(-x)-11 =-7x^5+15x^4+x^3+4x^2+6x-11
anonymous
  • anonymous
2 sign changes in f(-x) so either 2 or 0 real negative zeros
anonymous
  • anonymous
so make a table with possible combinations of zeros
anonymous
  • anonymous
positive 3 3 1 1 negative 2 0 2 0 complex 0 2 2 4
anonymous
  • anonymous
each column must add to 5 because it is a 5th degree polynomial with 5 zeros
anonymous
  • anonymous
if there are 3 positive real zeros, there can be either 2 or 0 negative real zeros
anonymous
  • anonymous
if there are 3 positive real zeros and 0 negative real zeros, the rest must be complex conjugates
anonymous
  • anonymous
yw

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