According to Descartes' Rule of Signs, can the polynomial function have exactly 4 positive real zeros, including any repeated zeros? Choose your answer based on the rule only. h(x) = x^4 - x^3 - 7x^2 + 6x - 1 Choices: (A)yes (B)no

Question

According to Descartes' Rule of Signs, can the polynomial function have exactly 4 positive real zeros, including any repeated zeros? Choose your answer based on the rule only.    h(x) = x^4 - x^3 - 7x^2 + 6x - 1     Choices: (A)yes (B)no

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Count Sign Changes: Count the number of sign changes in the coefficients of h(x) = x^4 - x^3 - 7x^2 + 6x - 1. Coefficients: 1, -1, -7, 6, -1. Sign changes: 1 to -1 (one change), -7 to 6 (second change), 6 to -1 (third change). Total sign changes: 3.Descartes' Rule of Signs: According to Descartes' Rule of Signs, the number of positive real zeros is either equal to the number of sign changes or less than that by an even number. With 3 sign changes, the possible numbers of positive real zeros are 3 or 1.Check Possibility: Check if having exactly 4 positive real zeros is possible. Since the possible numbers of positive real zeros are 3 or 1, having exactly 4 positive real zeros is not possible.

According to Descartes' Rule of Signs, can the polynomial function have exactly $4$ positive real zeros, including any repeated zeros? Choose your answer based on the rule only. $\newline$ $h(x) = x^4 - x^3 - 7x^2 + x - 1$ $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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