Chapter 6.1, Problem 73SR

To determine

To find: The rational zeroes of the given function.

Answer to Problem 73SR

The rational zeroes of the given function is $x=\frac{1}{2}$ .

Explanation of Solution

Given:

The given function is

  $f\left(x\right)=-4x^4-x^2-x+1$

Calculation:

Calculate the rational zeroes of the function.

For a polynomial function with integer coefficients.

  $a_n{x}^n+a_{n-1}{x}^{n-1}\mathrm{....}{a}_0$

The rational roots can be found by checking for $\pm \frac{\text{dividers of }{a}_0}{\text{dividers of }{a}_n}$

Here

  $\begin{array}{l}{a}_0=1\\ a_n=-4\end{array}$

The dividers of $a_0=1$

The dividers of $a_n=1,2,4$

The possible roots are:

  $\pm \frac{1}{1,2,4}$

Put these values in the given function and validate the roots. The root is $\frac{1}{2}$ .

Therefore, the rational zeroes of the given function is $x=\frac{1}{2}$ .