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If $f(x)=x^7-3x^4+2x^3-k=0$, $k>0$

So putting x=-x in the equation, I am getting two sign changes. However, the problem in my book says three. Also, will the answer depend on the little condition given, ($k>0$)?

snowfall512
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Zlatan
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    Check again. There are 3 changes in signs for $f(x)$ and no change in signs for $f(-x)$. The condition $k>0$ is important. – Isko10986 Nov 15 '16 at 01:26
  • Oh got it. I took the sign change to be the relative sign change in each term in replacing x by -x. But thanks now I got it. – Zlatan Nov 15 '16 at 01:30
  • Juat supposing, if I had 1 change in $f(-x)$ then what would be the total number of sign changes? – Zlatan Nov 15 '16 at 01:32
  • I am not really sure about that "total number of sign changes". Please refer to examples in your reference. Only thing for sure is that, the number of changes of signs in $f(x)$ is the maximum number of positive roots of $f(x)=0$; the number of changes of signs in $f(-x)$ is the maximum number of negative roots of $f(x)=0$ – Isko10986 Nov 15 '16 at 01:36

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