Chapter 4.2, Problem 44PPS

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 44PPS

  $-5$ and $3\text{and}4$ .

Explanation of Solution

Given:

The given equation is $-35=-3x-2x^2$ .

Calculation:

The given equation is expressed as

  $2x^2+3x-35=0\left\{\text{add}35\text{ on both the sides}\right\}$ .

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

  

Looking at the graph, the parabola crosses the x -axis, therefore, there is two real solution for the graph.

The axis of symmetric is

  $\begin{array}{l}x=\frac{-b}{2a}\left\{\text{equation for symmetry}\right\}\\ x=\frac{-\left(3\right)}{2\left(2\right)}\{\text{substitutes these value}}\\ x=\frac{-3}{4}=-0.75\end{array}$

Now write the table for the given function.

$x$	$-5$	$-4$	$-0.75$	$3$	$4$
$f\left(x\right)$	$0$	$-15$	$-36.125$	$-8$	$9$

Based on the table and the graph, there is one zero in the function which is $-5$ and one x -intercept indicate that the other solution is between $3\text{and}4$ .

Hence, the solution of the given equation is between $-5$ and $3\text{and}4$ .