Concept explainers
To solve the given equation using graphing.
Answer to Problem 25PPS
The values of x are -4.2 and 2.2.
Explanation of Solution
Given information :
The function provided is
Formula used :
The given equation would be graphed as a function and the points of x-intercepts would be the results. For these points, the x-coordinate shall serve the purpose of the results.
Since the roots are not on points that are integers, use the approximation method to compute the roots.
Calculation :
The graph of the given equation is
In this, the parabola one x-intercept is between -5 and -4. The other x-intercept is between 2 and 3.
To find the roots, make a table of values for x in between these points with intervals on 0.1 . The value of x that is result closest to 0 will be the roots of the equation.
Table of values in between -5 and -4
X | -4.9 | -4.8 | -4.7 | -4.6 | -4.5 | -4.4 | -4.3 | -4.2 | -4.1 |
y | 5.21 | 4.44 | 3.69 | 2.96 | 2.25 | 1.56 | 0.89 | 0.24 | -0.39 |
Table of values in between 2 and 3
x | 2.1 | 2.2 | 2.3 | 2.4 | 2.5 | 2.6 | 2.7 | 2.8 | 2.9 |
y | -0.39 | 0.24 | 0.89 | 1.56 | 2.25 | 2.96 | 3.69 | 4.44 | 5.21 |
In the tables, the value of y that is closest to 0 is 0.24. Their corresponding x values would be the roots.
Thus, -4.2 and 2.2 are the roots.
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