Work Step by Step
Given: $f(x)=x^4+6x^3-x^2+7x-8$ We can see that there are 3 sign changes. There might be 3 or 1 positive zeros. $f(-x)=(-x)^4+6(-x)^3-(-x)^2+7(-x)-8=x^4-6x^3+x^2-7x-8$ There is one sign change here. Thus, there is one zero. The possible combinations: 3 positive real, 1 negative real 1 positive real, 1 negative real, 2 imaginary.