Using complete sentences, describe how you would analyze the zeros of the polynomial function f(x) = –3x5 – 8x4 +25x3 – 8x2 +x – 19 using Descartes’ Rule of Signs. (2 points)
With f(x) = -3x^5 - 8x^4 + 25x^3 - 8x^2 + x - 19, we see that:
f(-x) = 3x^5 - 8x^4 - 25x^3 - 8x^2 - x - 19.
Then, f(x) has 4 sign changes and f(-x) has 1 sign change. [ Thus, f(x) has either 4, 2, or 0 positive real zeroes and f(x) has 1 negative real zero. ]
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