find the real solutions of each equation by graphing.
2x^4=9x^2-4
15x^4=11x^3 + 14x^2
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To find the real solutions of each equation by graphing, follow these steps:
1. Start by rewriting each equation in the form where one side is equal to zero:
Equation 1: 2x^4 - 9x^2 + 4 = 0
Equation 2: 15x^4 - 11x^3 - 14x^2 = 0
2. Plot the graph of each equation on a coordinate plane. To do this, create a table of x and y values by plugging in different values for x and calculating the corresponding y values using the equation. For example, for Equation 1, choose a range of x values like -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Calculate the corresponding y values for each x value and plot the points (x, y) on the graph.
3. Connect the plotted points with a smooth curve. This will give you the graph of the equation.
4. Identify the x-values where the graph intersects or touches the x-axis. These x-values represent the solutions to the equations.
For Equation 1: 2x^4 - 9x^2 + 4 = 0
By graphing the equation, you will find the x-values where the graph touches or crosses the x-axis. These x-values are the real solutions to the equation.
For Equation 2: 15x^4 - 11x^3 - 14x^2 = 0
By graphing the equation, you will find the x-values where the graph touches or crosses the x-axis. These x-values are the real solutions to the equation.