Answer
See below
Work Step by Step
Given: $f(x)=x^7+10x^6-5x^4+12x^3-17$
We can see that there are 3 sign changes. There might be 3 or 1 positive zeros.
$f(-x)=(-x)^7+10(-x)^6-5(-x)^4+12(-x)^3-17\\=-x^7+10x^6-5x^4-12x^3-17$
There are 2 sign changes here. Thus, there can be 2 or one zeros.
The possible combinations:
3 positive real, 2 negative real, 2 imaginary
3 positive real, 4 imaginary
1 positive real, 2 negative real, 2 imaginary
1 positive real, 6 imaginary
