Question

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

Answer 1

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.