Concept explainers
To solve the given equation using graphing.
Answer to Problem 27SGR
The roots of x are -4.6 and 0.6 .
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 0 and 1.
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 | 1.41 | 0.84 | 0.29 | -0.24 | -0.75 | -1.24 | -1.71 | -2.16 | -2.59 |
Table of values in between 0 and 1
x | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
y | -2.59 | -2.16 | -1.71 | -1.24 | 0.75 | -0.24 | 0.29 | 0.84 | 1.41 |
In the tables, the value of y that is closest to 0 is -0.24. Their corresponding x values would be the roots.
Thus, -4.6 and 0.6 are the roots.
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