Tell the maximum number of zeros that the polynomial function may have. then use descartes' rule of signs to determine how many positive and how many negative real zeros the polynomial function may have. do not attempt to find the zeros. f left parenthesis x right parenthesis equals negative 4 x superscript 7 baseline plus x cubed minus x squared plus 5

F(x) = -4x^7 +x^3 -x^2 +5

a) It is a degree 7 polynomial, so will have 7 zeros (some may be repeated).

b) has 3 sign changes, so 1 or 3 positive real zeros. If odd powers have their signs reversed, the signs are changed to +--+, so there are 2 sign changes. There will be 0 or 2 negative real zeros.

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There is actually 1 positive real zero and 0 negative real zeros. This means there are 3 conjugate pairs of complex zeros.

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