Question

Use the rational zeros theorem to list all possible rational zeros of the following. f(x) = -9 - 8x + 4x² - 9x³ Be sure that no value in your list appears more than once.

Answer 1

The rational zeros theorem states that the possible rational roots of a polynomial are given by the factors of the constant term divided by the factors of the lead coefficient.

In the given polynomial f(x), the constant term is -9 and the lead coefficient is also -9.

The factors of -9 are:

`\pm1,\pm3,\pm9`

Therefore the possible rational roots are:

`\begin{gathered} possible\text{ }rational\text{ }roots=(\pm1,\pm3,\pm9)/(\pm1,\pm3,\pm9)\\ \\ =\pm(1)/(9),\pm(1)/(3),\pm1,\pm3,\pm9 \end{gathered}`