Solve each equation by graphing. Where necessary, round to the nearest hundredth
x^4+2x-3= 0
To solve the equation x^4 + 2x - 3 = 0 by graphing, you can follow these steps:
1. Rewrite the equation in the standard form: x^4 + 2x - 3 = 0
2. Start by creating a table of x and y values. Choose a range of x values and substitute them into the equation to find the corresponding y values. Let's use x values from -2 to 2.
x | y
----------------
-2 |
-1 |
0 |
1 |
2 |
3. Substitute each x value into the equation to find the corresponding y value. For example, when x = -2:
(-2)^4 + 2(-2) - 3 = y
16 - 4 - 3 = y
9 = y
4. Add the calculated y values to the table.
x | y
----------------
-2 | 9
-1 |
0 |
1 |
2 |
5. Plot the points (x, y) from the table on the coordinate plane.
6. Draw a smooth curve that passes through the plotted points to form the graph of the equation.
7. Look for the x-values where the curve intersects or is closest to the x-axis. These are the solutions to the equation.
8. Estimate the x-values where the curve intersects the x-axis by reading the approximate coordinates of the points of intersection from the graph.
9. Round the estimated x-values to the nearest hundredth to find the solutions to the equation.
However, as the equation is a quartic (degree 4) equation, it may not be easy to graph it accurately by hand. In such cases, it is advisable to use alternative methods like factoring, completing the square, or using numerical methods to find the solutions more accurately.