Question

Math help.

Answer 1

the total number of roots is equal to the highest power (in this case, 5)

to calculate the potential number of positive roots, count the number of sign changes (the first term is negative, then the term after that is positive, so that's 1 sign change, then with -x it goes back to negative, so that's another sign change, and it doesn't change anymore after that, so 2 changes, so 2 potential positive roots).

however, you could also potentially have 2 complex roots (complex roots always come in pairs) so another possibility is 0 positive 2 complex.

for negative roots, calculate f(-x) instead (replace every x with -x and re-calculate, being careful about signs) and repeat the process for the # of sign changes. also repeat the part where you subtract 2 at a time to get pairs of complex roots.

list all the possibile combinations of roots.

Answer 2

Oh, thats called descarte's rule of sign right? Thanks.