Concept explainers
To solve the given equation using graphing.
Answer to Problem 29SGR
The roots of x are -0.8 and 3 .
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.
If the roots are not on points that are integers, use the approximation method to compute the roots.
Else, put the x-intercept value in the equation. If the left-hand and right-hand sides of the equations match, it is a success and those will be the values of x.
Calculation :
The graph of the given equation is
The zeroes in the graph are at
In this, the parabola one x-intercept is between -1 and 0.
To find the root, 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 -1 and 0
X | -0.9 | -0.8 | -0.7 | -0.6 | -0.5 | -0.4 | -0.3 | -0.2 | -0.1 |
Y | 1.56 | -0.76 | -2.96 | -5.04 | -7 | -8.84 | -10.56 | -12.16 | -13.64 |
In the tables, the value of y that is closest to 0 is -0.76. Their corresponding x values would be the roots.
Thus, -0.8 is the first root.
For the second root, check if the value of the x-coordinate matches both sides of the given equation.
Put these values in the given equation to recheck.
Putting
Simplifying
Hence second value of x is a success.
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Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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