Question

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x) = 5x? - 9x³ + 14x² - 18x + 8 ? 1, $rac{4}{5}$: f(x) = (x - 1)(5x - 4)(x² + 2) ? -2, -1, 1, -$rac{4}{5}$: f(x) = (x - 1)(5x + 4)(x + 1)(x + 2) ? 2, $rac{4}{5}$: f(x) = (x - 2)(5x - 4)(x² + 1) ? -2, -1, 1, $rac{4}{5}$: f(x) = (x - 1)(5x - 4)(x + 1)(x + 2)

          Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the
polynomial function. Use the zeros to factor f over the real numbers.
f(x) = 5x? - 9x³ + 14x² - 18x + 8
? 1, $rac{4}{5}$: f(x) = (x - 1)(5x - 4)(x² + 2)
? -2, -1, 1, -$rac{4}{5}$: f(x) = (x - 1)(5x + 4)(x + 1)(x + 2)
? 2, $rac{4}{5}$: f(x) = (x - 2)(5x - 4)(x² + 1)
? -2, -1, 1, $rac{4}{5}$: f(x) = (x - 1)(5x - 4)(x + 1)(x + 2)

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the
polynomial function. Use the zeros to factor f over the real numbers.
f(x) = 5x? - 9x³ + 14x² - 18x + 8
? 1, rac45: f(x) = (x - 1)(5x - 4)(x² + 2)
? -2, -1, 1, -rac45: f(x) = (x - 1)(5x + 4)(x + 1)(x + 2)
? 2, rac45: f(x) = (x - 2)(5x - 4)(x² + 1)
? -2, -1, 1, rac45: f(x) = (x - 1)(5x - 4)(x + 1)(x + 2)

Added by Mark M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shima Shaw

Step 1

The polynomial function f = 54.93x^2 + 142x - 18x + 8 has two sign changes in the coefficients. Therefore, there are either two positive real zeros or zero positive real zeros. Show more…

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Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f = 54.93x^2 + 142x - 18x + 8 0.1, 1 (x = x - 15x - 4(2 + 2) O2.1.1. - (x = x - 1x^5 + x^4 + 2) O2. f(x) = -25x^4 + 2x^2 + 1 2. -1, 1, f(x) = x - 1(5x - 4x + 1 + 2)