anonymous
  • anonymous
List all the real and imaginary zeros of f(x) = x^3+x^2+ 13x - 15... 1 is a zero of the function
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
all possible rational roost are number of the form \(\frac{p}{q}\) where \(p\) divides the constant ( in your case 15) and \(q\) divides the leading coefficient, in your case 1
anonymous
  • anonymous
so the possibilites are \[\pm1,\pm3,\pm5,\pm15\]
anonymous
  • anonymous
since you know 1 is a zero, you can factor it as \[(x-1)(\text{something})\] and you can find the something by dividing, by synthetic division or by thinking

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anonymous
  • anonymous
and to find all real and imaginary zeros
anonymous
  • anonymous
in this case you get \[(x-1) (x^2+2 x+15)\] and the second part you can find the zeros using the quadratic formula they are complex

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