Question

Use the rational zeros theorem to list all possible rational zeros of the following.

Answer 1

The given function is:

`g(x)=-25x^3-5x^2-2x-1`

The theorem states that the factors are p/q where p is the factors of the last term (constant term) and q is the factors of the leading coefficient.

Here the leading coefficient is -25 and the constant term is -1.

The factors are listed below:

`\begin{gathered} -25\Rightarrow\pm25,\pm5,\pm1\Rightarrow q \\ -1=\pm1\Rightarrow p \end{gathered}`

So the value of p/q can be the values shown below:

`(p)/(q)\Rightarrow\pm(1)/(25),\pm(1)/(5),\pm1`

Hence the possible zeroes of the given function are:

`\pm(1)/(25),\pm(1)/(5),\pm1`