Chapter 8.8, Problem 37WE

(a)

To determine

To find: Thevalue of $f\left(0\right)$ .

Answer to Problem 37WE

The value of $f\left(0\right)$ is $8$ .

Explanation of Solution

Given information:

The given equation is,

  $f\left(x\right)=x^2-6x+8$

The value of $f\left(0\right)$ is calculated as,

  $\begin{array}{l}f\left(x\right)=x^2-6x+8\\ f\left(0\right)={\left(0\right)}^2-6\left(0\right)+8\\ f\left(0\right)=8\end{array}$

Thus, the value of $f\left(0\right)$ is $8$ .

(b)

To determine

To find: The zeros of $f$ .

Answer to Problem 37WE

The zeros of $f$ are $2\text{and}4$ .

Explanation of Solution

Given information:

The given equation is,

  $f\left(x\right)=x^2-6x+8$

The value of $f\left(0\right)$ is calculated as,

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

Simplify further,

  $x=2,4$

Thus, the zeros of $f$ are $2\text{and}4$ .