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24 votes
24 votes
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

User Rrrokhtar
by
3.2k points

2 Answers

21 votes
21 votes

Answer:

B

Explanation:

on edge

User Peter Dongan
by
2.6k points
19 votes
19 votes

Answer:

-1

Explanation:

The attached result from a graphing calculator shows the other root to be ...

x = -1

__

The "system of equations" consists of one equation for the left side function, and one equation for the right side function. The graphs of the two equations intersect at the point where the left and right parts of the given equation are equal to each other. The graphs intersect at x=-1.

__

Additional comment

We prefer to subtract one side of the equation from the other, so we have a single function whose value is 0 at the root of interest. Here, that would be ...

(x^3 +x^2) -(-9x -9) = 0

x^2 +x^2 +9x +9 = 0

We would graph y = x^3 +x^2 +9x +9 and have the graphing calculator identify the x-intercept. This is shown in the second attachment. No "system of equations" is required for this.

The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots-example-1
The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots-example-2
User Binkan Salaryman
by
2.8k points
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