Question

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.

Answer 1

@campbell_st

Answer 2

@kirbykirby

Answer 3

@freckles

Answer 4

The number of zeroes for a polynomial will be the same as the highest power of your polynomial, which comes from the fundamental theorem of algebra.

Answer 5

so 5 zeroes.

Answer 6

yup

Answer 7

Thank you @kirbykirby and now to find the positive and negative roots.

Answer 8

Now for the max number of positive real roots..
You look at the polynomial \(p(x)\) and look at the sign changes: