Question

Given f(x) = 4x^8 - 6x^2 + 3x - 7, how many sign changes are there in the coefficients of f(x-)?

Answer 1

We have the expression:

`f(x)=4x^8-6x^2+3x-7`

And the question wants to know how many sign changes we have when we plot -x in the function, to solve this we need to remember that:

`(-1)^n=1\text{ when n is even and }(-1)^n=-1\text{ when n is odd}`

So, lets solve:

`f(-x)=4(-x)^8-6(-x)^2+3(-x)-7\rightarrow f(-x)=4x^8-6x^2-3x-7`

So, only the sign of 3 changed, so we have only one change.