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According to Descartes' rule of signs, there can be either two real positive zeros (roots), or none. According to the same rule, by consideration of sign changes in f(-x), there can be either two real negative zeros, or none. Overall, then, there could be 0, 2, 4, 6 or even 8 imaginary zeros (occurring as conjugate pairs), depending on however many real roots there turn out to be; for the latter, I recommend exploring the function on a graphing calculator. Call Now to Set Up Tutoring: (888) 888-0446 All Precalculus ResourcesDetermine the possible number of Positive and Negative Real Zeros of the polynomial using Descartes' Rule of Signs Possible Answers: Positive zeroes: Negative zeroes: Positive zeroes:  Negative zeroes: Positive zeroes: Negative zeroes: Positive zeroes: Negative zeroes: Correct answer: Positive zeroes: Negative zeroes: Explanation: In order to determine the positive number of real zeroes, we must count the number of sign changes in the coefficients of the terms of the polynomial. The number of real zeroes can then be any positive difference of that number and a positive multiple of two. For the function there are four sign changes. As such, the number of positive real zeroes can be In order to determine the positive number of real zeroes, we must count the number of sign changes in the coefficients of the terms of the polynomial after substituting for The number of real zeroes can then be any positive difference of that number and a positive multiple of two. After substituting we get and there is one sign change. As such, there can only be one negative root. Nadia
University of Connecticut, Bachelor in Arts, General Studies. Bhupinder Panjab University, Bachelor of Engineering, Biotechnology. Hamburg University of Technology, Master of Science, Chemical Engi... David University of California-Los Angeles, Bachelor of Science, Applied Mathematics. University of Southern California, Masters in... All Precalculus ResourcesHow do you find the number of positive and negative zeros of a function?In order to determine the positive number of real zeroes, we must count the number of sign changes in the coefficients of the terms of the polynomial. The number of real zeroes can then be any positive difference of that number and a positive multiple of two.
What is Descartes rule of signs calculator?The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is less than it by an even number.
How do you find the number of positive roots?For the number of positive real roots, look at the polynomial, written in descending order, and count how many times the sign changes from term to term. This value represents the maximum number of positive roots in the polynomial.
How do you find the number of negative roots?The number of negative roots of f(x) is equal to the number of positive roots of g(x) = f(-x) = 0. Therefore the negative real roots of the given equation are two or zero. To determine the real roots of equation (1) one has to determine the number of sign changes which occur in the equation.
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Find number of positive and negative zeros calculator
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