Use the following to answer questions :
p(x) = x 4 - 5x 3 + 5x 2 + 5x - 6
-Apply Descartes's rule of signs to count the possible number of positive, negative, and complex roots (organize a table).

Question

Quizplus · Accepted Answer

Using Descartes's rule of signs, we count the number of positive and negative roots as follows: - The number of sign changes in p(x) is 2 (from +5x to -6, and from -5x³ to +5x²), so there are at most 2 positive roots. - The number of sign changes in p(-x) is 1 (from -5x³ to +5x²), so there is at most 1 negative root. - The number of non-real roots (complex roots) is either 0 or even (because the coefficients are all real). Therefore, the best choice is C since it satisfies all of these conditions.

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