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3 years ago

What are the real and complex solutions of the polynomial equation X^3-216=0

Mathematics

1 answer:

vazorg [7]3 years ago

3 0

Answer:

$6,\ -3+3\sqrt{3}i,\ -3-3\sqrt{3}i$

Step-by-step explanation:

Factor the equation $x^3-216=0$ using formula for difference of the cubes:

$x^3-216=(x-6)(x^2+6x+36),$

then

$x-6=0\ or\ x^2+6x+36=0.$

1. The equation $x-6=0$ has real solution $x=6.$

2. The equation $x^2+6x+36=0$ has negative discriminant $D=6^2-4\cdot 36=36-144=-108,$ then it has two complex solutions

$x_{1,2}=\dfrac{-6\pm 6\sqrt{3}i}{2}=-3\pm3\sqrt{3}i.$

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3 years ago

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Step-by-step explanation:

First, we need to calculate what each answer choice will equal.

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3 years ago

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3 years ago

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Answer with Step-by-step explanation:

We are given that

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