Find the real solutions of the following equation by graphing.
x^3-5x^2+4x=0
To graph the equation, we can start by factoring out an x from each term:
x(x^2 - 5x + 4) = 0
Now we can set each factor equal to zero and solve for x:
x = 0
x^2 - 5x + 4 = 0
To graph the equation, we can create a table of values:
x | y
-------
-2 | 0
-1 | 0
0 | 0
1 | 0
2 | 0
Plotting these points on a graph, we can see that the graph of y = x^3 - 5x^2 + 4x intersects the x-axis at x = 0, x = 1, and x = 4.
Therefore, the real solutions of the equation x^3 - 5x^2 + 4x = 0 are x = 0, x = 1, and x = 4.