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The graph of y=x^3-2x^2-3x is shown in Figure 1. Based on the graph, what do you think are the solutions of the equation x^3-2x^2-3x=0? Confirm that your values are solutions by substituting them in place of x in the equation x^3-2x^2-3x=0 to see that you get a true statement.

Sagot :

The solutions to the given equation are x = -1, x = 0 and x = 3

Graph of Cubic Equation

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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