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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

Sagot :

sqdancefan

Answer:

  -1

Step-by-step explanation:

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

  x = -1

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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.

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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.

View image sqdancefan
View image sqdancefan
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