Question

What are the possible number of negative zeros of f(x) = 2x7 – 2x6 + 7x5 – 7x4 – 4x3 + 4x2 ?
is it 2 ?

Answer 1

You're doing Descartes' Rule of Signs?

rewrite the equation as f(-x) (just flip the signs of the odd-powered terms)
\[f(-x) = -2x^7-2x^6-7x^5-7x^4+4x^3+4x^2\]Count sign changes
----++
1 sign change
so 1 negative real root/zero