Question

The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots plus-or-minus 3 i. What is the other root? Use a graphing calculator and a system of equations.

–9
–1
0
1

Answer 1

so, have you used your calculator?

Answer 2

x cubed + x squared = negative 9 x minus 9

why not ....
x^3 + x^2 = 9x - 9
x^3 + x^2 - 9x + 9 = 0
you know x^2 + 9 is a factor, so
by either long division or synthetic division .....
x^3 + x^2 - 9x + 9 = 0
--> (x^2+9)(x+1) = 0
so the other root is -1

Answer 3

[AI-generated answer — Step-by-Step Bot]

To find the other root, we can use a graphing calculator and a system of equations.

Step 1: Input the given polynomial equation into the graphing calculator.

Step 2: Set the equation equal to zero by subtracting -9x - 9 from both sides, resulting in the equation x^3 + x^2 + 9x + 9 = 0.

Step 3: Use the graphing calculator to plot the graph of this equation.

Step 4: The graph should show the two complex roots, plus-or-minus 3i, on the imaginary axis.

Step 5: Since complex roots occur in conjugate pairs, the other root must also be a complex number. Therefore, there is no real root for this equation.

Thus, the answer is 0.

Answer 4

[AI-generated answer — Explain Bot]

To find the other root of the polynomial equation x^3 + x^2 = -9x - 9, we can use a graphing calculator and a system of equations.

Step 1: Enter the equation into the graphing calculator.
- On the graphing calculator's screen, enter the equation as: y1 = x^3 + x^2 + 9x + 9.

Step 2: Graph the equation.
- Graph the equation on the calculator using the "y=" function.

Step 3: Find the x-coordinate of the other root.
- To find the x-coordinate of the other root, use the cursor or trace function on the graphing calculator to find the point where the graph intersects the x-axis.
- This x-coordinate is the value of the other root.

Step 4: Set up a system of equations.
- Let the other root be represented by the variable "a." We know that the complex roots are ±3i.
- Therefore, we can set up the following equation: (x - 3i)(x + 3i)(x - a) = 0.

Step 5: Expand and simplify the equation.
- Expand the equation using the difference of squares:
(x^2 + 9)(x - a) = 0.
x^3 - ax^2 + 9x - 9a = 0.

Step 6: Compare coefficients.
- Compare the coefficients of the expanded equation with the original equation: x^3 + x^2 = -9x - 9.
- From this comparison, we can determine that a = -1.

Therefore, the other root is -1.