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EleoNora [17]
3 years ago
15

What are the real and complex solutions of the polynomial equation x^3 - 64 = 0

Geography
2 answers:
Anna35 [415]3 years ago
4 0

Note that, x = 4 is a solution for the equation.

Then, you can use this value to factored the equation as follows

x^3 - 64 = (x-4)(x^2  +4x  +16) = 0

Now you need solve

x^2 +4x +16 = 0

x = \frac{-b \pm \sqrt{b^2 -4ac} } {2a} =  \frac{-4 \pm \sqrt{16 -64} } {2} = \frac{-4 \pm \sqrt{-48} } {2}  = \frac{-4 \pm 4i\sqrt{3} } {2} =-2 \pm2i\sqrt{3}

Therefore, the solutions are

4, -2+2i\sqrt{3}, -2-2i\sqrt{3}.

son4ous [18]3 years ago
4 0

Answer:

The answer is C on connexus :)

Explanation:

Your welcome, saves time:)

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