what is the positive solution of the equation 3x^2 - 5x - 7 =0? solve by using a table or by graphing. if necessary, round your answer to the nearest hundredth.
To find the positive solution of the equation 3x^2 - 5x - 7 = 0, we can solve it either by using a table or by graphing.
Using a table:
1. First, arrange the equation in the standard quadratic form: ax^2 + bx + c = 0. In this case, a = 3, b = -5, and c = -7.
2. Create a table with columns for x and y.
3. Choose values for x and substitute them into the equation to find the corresponding y-values.
4. Fill in the table until you find a value of y that is close to zero.
5. The x-value corresponding to that y-value is the positive solution.
Using graphing:
1. Graph the equation 3x^2 - 5x - 7 = 0 on a coordinate plane.
2. On the graph, identify the x-coordinate(s) at which the graph intersects the x-axis. One of these x-coordinates will correspond to the positive solution.
Both methods lead to the same result, but graphing can provide a visual representation of the solutions. Now, let's solve the equation using a table.
Using a table:
1. Choose some values for x and substitute them into the equation to find the corresponding y-values. For simplicity, let's choose values of x ranging from -1 to 2:
- For x = -1, substitute -1 into the equation: 3(-1)^2 - 5(-1) - 7 = 3 + 5 - 7 = 1 - 7 = -6.
- For x = 0, substitute 0 into the equation: 3(0)^2 - 5(0) - 7 = 0 - 0 - 7 = -7.
- For x = 1, substitute 1 into the equation: 3(1)^2 - 5(1) - 7 = 3 - 5 - 7 = 1 - 7 = -6.
- For x = 2, substitute 2 into the equation: 3(2)^2 - 5(2) - 7 = 12 - 10 - 7 = 5.
2. Fill in the table with the x and y-values:
| x | y |
| -1 | -6 |
| 0 | -7 |
| 1 | -6 |
| 2 | 5 |
3. From the table, we can see that when x = 2, the value of y is positive (5), which implies that x = 2 is the positive solution.
Therefore, the positive solution of the equation 3x^2 - 5x - 7 = 0, rounded to the nearest hundredth, is x = 2.