is-it-125x-3-1-3-a-polynomial-

Question Number 180730 by sciencestudent last updated on 16/Nov/22

i s i t \sqrt[3]{125 x^{3}} a p o l y n o m i a l ?

Answered by Frix last updated on 16/Nov/22

No . But for x \in R it is equal to a polynomial :

\sqrt[3]{125 x^{3}} = 5 x

Because in R we define \sqrt[3]{- r} = - \sqrt[3]{r} wherelse

for x \in C we have x = r e^{i θ} and \sqrt[3]{x} = \sqrt[3]{r} e^{i \frac{θ}{3}} .

in R \sqrt[3]{- 1} = - \sqrt[3]{1} = - 1

in C \sqrt[3]{- 1} = \sqrt[3]{1} e^{i \frac{π}{3}} = \frac{1}{2} + \frac{\sqrt{3}}{2} i

Commented by MJS_new last updated on 16/Nov/22

{you}^{'} re right

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