The solutions to the given equation are x = -1, x = 0 and x = 3
From the question, we are to determine the solution of the given equation.
The given equation is
x³ -2x² -3x = 0
The graph of the function y = x³ -2x² -3x is shown below
The solutions of the equation x³ -2x² -3x = 0 are the values where the graph cuts the x-axis
From the graph, we can observe that
The curve cuts the x-axis at x = -1, x = 0 and x = 3
Hence, the solutions to the given equation are x = -1, x = 0 and x = 3
Testing the solutions
For x = -1
x³ -2x² -3x = 0
(-1)³ -2(-1)² -3(-1) = 0
-1 -2(1) +3 = 0
-1 -2+3 = 0
-3+3 = 0
0 = 0
For x = 0
x³ -2x² -3x = 0
(0)³ -2(0)² -3(0) = 0
0 - 0 - 0 =0
0 = 0
For x = 3
x³ -2x² -3x = 0
(3)³ -2(3)² -3(3) = 0
27 -2(9) - 9 = 0
27 -18 - 9 = 0
0 = 0
Since, all the statements are true, then values are solutions of the equation.
Learn more on Graph of Cubic equations here: https://brainly.com/question/8878887
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