Explanation
Given
[tex]w^3-1000=0[/tex]
We will have;
[tex]\begin{gathered} w^3=1000 \\ \mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2} \\ therefore;\text{ }w=\sqrt[3]{1000},\:w=\sqrt[3]{1000}\frac{-1+\sqrt{3}i}{2},\:w=\sqrt[3]{1000}\frac{-1-\sqrt{3}i}{2} \\ hence;w=10,w=10\times\frac{-1+\sqrt{3}i}{2},\:w=10\times\frac{-1-\sqrt{3}i}{2} \\ w=10,\:w=-5+5\sqrt{3}i,\:w=-5-5\sqrt{3}i \end{gathered}[/tex]
Answer: Option D
