Question

What is the possible number of negative real roots of the function

f(x) = x5 − 2x3 + 7x2 + 2x − 2?

Answer 1

using I forgot who's thingummy math thing
change sign thing
ah, descartes rule of signs, thank you google


replace x with -x
simplify
count the number of times the sign changes between terms
if the number is 2 or more, keep subtracting 2 until you reach 0 or 1
so

if we replace x with -x we get
-x^5+2x^3+7x^2-2x-2
(-), (+), (+), (-), (-)
2 changes
2-2=0

so 2 or 0 possible negative real roots