The polynomial p(x) = x^{5} − 9x^{4 }+ 13x^{3} + 57x^{2} − 86x − 120 has a total of zeroes. It can have a maximum of positive real roots and a maximum of negative real roots.

Since it is 5th order polynomial it has a total of 5 zeroes.

Using Descartes' Rule of Signs,

It can have a maximum of 3 positive real roots

and a maximum of 2 negative real roots

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