Question

Can you please check my work?

Use Decartes Rule of signs to determine the possible number of postive and negative real zeros for the given function.

1. f(x)=-7x^9+x^5-x^2+6
This is what I did:
There are 2 sign changes

f(-x)=-7(-x)^9+(-x)^5-(-x)^2+6
There are 2 sign changes

So, are there 2 or 0 positive zeros, 2 or 0 negative zeros?

2. f(x)10x^3-8x^2+x+5
There are 2 sign changes

f(-x)=10(-x)^3-8(-x)^2+(-x)+5
There are 2 sign changes

So, are there 2 or 0 positive zeros, no negative zeros?

Answer 1

correct