Chapter 4.2, Problem 6CYU

To determine

To solve: the given equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.

Answer to Problem 6CYU

  $-2\text{and}-1$ and $5\text{and}6$ ..

Explanation of Solution

Given:

The given equation is $4x-x^2+8=0$ .

Calculation:

The given equation is expressed as $x^2-4x-8=0$ .

Now, graph the related quadratic function to show that x-intercept of the graph.

  

The axis of symmetry is:

  $\begin{array}{l}x=\frac{-b}{2a}\left\{\text{equation for symmetry}\right\}\\ x=\frac{-\left(-4\right)}{2\left(-1\right)}\{\text{substitutes these value}}\\ X=\frac{4}{-2}=2\{\text{simplify}}\end{array}$

Now write the table for the given function.

$x$	$-2$	$-1$	$2$	$5$	$6$
$f\left(x\right)$	$-4$	$3$	$12$	$3$	$-4$

Based on the table and the graph, the x-intercept of the graph indicate that one solution is between $-2\text{and}-1$ and the other solution is between $5\text{and}6$ .

Hence, the solution of the given equation is between $-2\text{and}-1$ and $5\text{and}6$ .