You can solve a polynomial equation by graphing each side of the equation separately on the same coordinate system. Then, to find the solution, just get the x-values at the point of intersection.
Example
Solve x^{3} + 3x^{2} = x + 3 by graphing
Step 1
Use a graphing calculator to graph y_{1} = x^{3} + 3x^{2} and y_{2} = x + 3 on the same screen. A portion of the graph is shown below. y_{1} is the graph shown in red and y_{2} is the graph shown in green.
Step 2
You can use either the graph above to locate the points of intersection or you can use the intersect feature in your calculator to find the x-values at the points of intersection.
The points of intersection are shown on the graph above with blue dots. The x-values give the solution. Therefore, the solutions are -3, -1, and 1.
Check
Show that -3, -1, and 1 are indeed solutions by plugging each value in the original solution.
x = -3
x^{3} + 3x^{2} = x + 3
(-3)^{3} + 3(-3)^{2} = -3 + 3
-27 + 3(9) = 0
-27 + 27 = 0
0 = 0
x = -1
(-1)^{3} + 3(-1)^{2} = -1 + 3
(-1)^{3} + 3(-1)^{2} = -1 + 3
-1 + 3(1) = 2
-1 + 3 = 2
2 = 2
x = 1
x^{3} + 3x^{2} = x + 3
(1)^{3} + 3(1)^{2} = 1 + 3
1 + 3(1) = 4
1 + 3 = 4
4 = 4
Sep 30, 22 04:45 PM