Chapter EP, Problem 6.6.16EP

To determine

To evaluate:

The value of the given number.

Answer to Problem 6.6.16EP

The value of given operation is $\left(x+\frac{1}{2}\right),\left(x-2\right)$ .

Explanation of Solution

Given:

The order of operation

  $6x^3-17x^2+6x+8$

Concept used:

Product means the answer to a multiplication problem

Sum means the total amount resulting from the addition of two or more numbers amounts or items

Quotient means a result obtained by dividing one quantity by another

Calculation:

The order of operation

The order of operation

  $=6x^3-17x^2+6x+\mathrm{8...................}\left(1\right)$

Putting $x=-\frac{1}{2},2$ in equation (1)

  $\begin{array}{l}f\left(x\right)=6x^3-17x^2+6x+8\\ f\left(-\frac{1}{2}\right)=6{\left(-\frac{1}{2}\right)}^3-17{\left(-\frac{1}{2}\right)}^2+6\left(-\frac{1}{2}\right)+8\\ f\left(-\frac{1}{2}\right)=6\left(-\frac{1}{8}\right)-17\left(\frac{1}{4}\right)-3+8\\ f\left(-\frac{1}{2}\right)=0\\ f\left(2\right)=6{\left(2\right)}^3-17{\left(2\right)}^2+6\left(2\right)+8\\ f\left(2\right)=6\left(8\right)-17\left(4\right)+12+8\\ f\left(2\right)=0\end{array}$

Therefore,

The value of given operation is $\left(x+\frac{1}{2}\right),\left(x-2\right)$ .