Chapter 6.1, Problem 68SR

To determine

To find: The rational zeroes of the given function.

Answer to Problem 68SR

The rational zeroes of the given function are $x=3,4,-\frac{1}{2}$ .

Explanation of Solution

Given:

The given function is $f\left(x\right)=2x^3-13x^2+17x+12$

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

  $\begin{array}{l}{a}_0=12\\ a_n=2\end{array}$

The dividers of $a_0=1,2,3,4,6,12$

The dividers of $a_n=1,2$

The possible roots are:

  $\pm \frac{1,2,3,4,6,12}{1,2}$

Put these values in the given function and validate the roots. The roots are

  $x=3,4,-\frac{1}{2}$

Therefore, the rational zeroes of the given function are $x=3,4,-\frac{1}{2}$ .