Chapter 4, Problem 38SGA

To determine

Find the location of the real zeroes of each function between consecutive integers.

Answer to Problem 38SGA

Between $0and1\&3and4$.

Explanation of Solution

Given information:

  $f\left(x\right)=x^2-4x+2$

Calculation:

Here, we have:

  $f\left(x\right)=x^2-4x+2$

Now, we can see that there are two complex zeros for this function.

We will use substitution, synthetic division, or table feature on a graphing calculator to solve this.

Now, we will test the possible zeros using synthetic division and the remainder theorem.

  $\begin{array}{llll}r\hfill & 1\hfill & -4\hfill & 2\hfill \\ -2\hfill & 1\hfill & -6\hfill & 14\hfill \\ -1\hfill & 1\hfill & -5\hfill & 7\hfill \\ 0\hfill & 1\hfill & -4\hfill & 2\hfill \\ 1\hfill & 1\hfill & -3\hfill & -1\hfill \\ 2\hfill & 1\hfill & -2\hfill & -2\hfill \\ 3\hfill & 1\hfill & -1\hfill & -1\hfill \\ 4\hfill & 1\hfill & 0\hfill & 2\hfill \end{array}$

Hence, the location of zero is between $0and1\&3and4$ .