Chapter 8.8, Problem 38WE

(a)

To determine

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

Answer to Problem 38WE

The value of $f\left(0\right)$ is $15$ .

Explanation of Solution

Given information:

The given equation is,

  $f\left(x\right)=x^2-8x+15$

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

  $\begin{array}{l}f\left(x\right)=x^2-8x+15\\ f\left(0\right)={\left(0\right)}^2-8\left(0\right)+15\\ f\left(0\right)=15\end{array}$

Thus, the value of $f\left(0\right)$ is $15$ .

(b)

To determine

To find: The zeros of $f$ .

Answer to Problem 38WE

The zeros of $f$ are $3\text{and}5$ .

Explanation of Solution

Given information:

The given equation is,

  $f\left(x\right)=x^2-8x+15$

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

  $\begin{array}{l}f\left(x\right)=x^2-8x+15\\ 0=x^2-5x-3x+15\\ x\left(x-5\right)-3\left(x-5\right)=0\\ \left(x-3\right)\left(x-5\right)=0\end{array}$

Simplify further,

  $x=3,5$

Thus, the zeros of $f$ are $3\text{and}5$ .