find the real solutions of each equation by graphing.
15x^4=11x^3+14x^2
wolframalpha.com is a good graphing site. Just type in your function or equation.
To find the real solutions of the equation 15x^4 = 11x^3 + 14x^2 by graphing, you can follow these steps:
Step 1: Rearrange the equation to bring all terms to one side.
15x^4 - 11x^3 - 14x^2 = 0
Step 2: Plot the function on a graph. Since this is a quartic equation, it will have a curved shape.
Step 3: To plot the graph, you can choose various values of x and calculate the corresponding y values using the equation. This will give you several points on the graph.
Step 4: Once you have plotted enough points, connect them to form a curve.
Step 5: Look for the points where the curve intersects the x-axis. These are the x-coordinates of the real solutions of the equation.
Step 6: Estimate the values of the x-coordinates where the curve crosses the x-axis and re-check by substituting these x-values back into the original equation to verify if they are indeed the real solutions.
Step 7: Repeat the process if there are more solutions.
By following these steps, you will be able to graphically determine the real solutions of the given equation.