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Dimas [21]
3 years ago
5

Which of the following is equivalent to the polynomial below?

Mathematics
1 answer:
Gnoma [55]3 years ago
6 0

Answer:

(x-(4+\sqrt{3}i))(x-(4-\sqrt{3}i))

Step-by-step explanation:

Consider the quadratic expression

x^2-8x+19

First, find its discriminant:

D=(-8)^2-4\cdot 1\cdot 19=64-76=-12

Note that i^2=-1, then D=12i^2.

Use quadratic formula to find the roots:

x_{1,2}=\dfrac{-(-8)\pm \sqrt{12i^2}}{2\cdot 1}=\dfrac{8\pm 2\sqrt{3} i}{2}=4\pm \sqrt{3}i

Now, given quadratic expression is equivalent to

(x-(4+\sqrt{3}i))(x-(4-\sqrt{3}i))\\ \\=(x-4-\sqrt{3}i)(x-4+\sqrt{3}i)

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