194k views
4 votes
Given f(x) = 4x^8 - 6x^2 + 3x - 7, how many sign changes are there in the coefficients of f(x-)?

1 Answer

0 votes

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.

User Mortz
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories