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Which of the following is the complete list of roots for the polynomial function f (x) = (x squared 6 x 8) (x squared 6 x 13)? –3 2i, –3 – 2i –2, –4 –2, –4, –3 2i, –3 – 2i –2, –4, –3 2i, 3 2i

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facundo3141592

The roots of the given polynomial function is {-4, -2, -3 + 2i, -3 - 2i}.

How to get the roots of the polynomial?

Here we have the polynomial function:

[tex]f(x) = (x^2 + 6x + 8)*(x^2 + 6x + 13)[/tex]

So we just need to find the roots of the two quadratic functions, to do that, we use Bhaskara's formula.

For the first one, we have:

[tex]x = \frac{-6 \pm \sqrt{6^2 - 4*8} }{2} \\\\x = \frac{-6 \pm 2}{2}[/tex]

So the two solutions are:

x = (-6 - 2)/2 = -4

x = (-6 + 2)/2 = -2

For the second quadratic we have:

[tex]x = \frac{-6 \pm \sqrt{6^2 - 4*13} }{2} \\\\x = \frac{-6 \pm 4i}{2}[/tex]

So the two solutions are:

x = -3 + 2i

x = -3 - 2i

Finally, the list is:

{-4, -2, -3 + 2i, -3 - 2i}

If you want to learn more about polynomials:

https://brainly.com/question/4142886

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