InterviewSolution
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InterviewSolution
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If `1,alpha_1,alpha_2,alpha_3,alpha_4` be the roots `x^5-1=0`, then value of `[omega-alpha_1]/[omega^2-alpha_1].[omega-alpha_2]/[omega^2-alpha_2].[omega-alpha_3]/[omega^2-alpha_3].[omega-alpha_4]/[omega^2-alpha_4]` is (where `omega` is imaginary cube root of unity) |
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Answer» `x^5-1=(x-1)(x-alpha_1)(x-alpha_2)(x-alpha_3)(x-alpha_4)` `w^5-1=(x-1)(w-alpha_1)(w-alpha_2)(w-alpha_3)(w-alpha_4)` `w^10-1=(w^2-1)(w^2-alpha_1)(w^2-alpha_2)(w^2-alpha_3)(w-alpha_5)` `(w^5-1)/(w^10-1)=((x-1)(w-alpha_1)(w-alpha_2)(w-alpha_3)(w-alpha_4))/((w^2-1)(w^2-alpha_1)(w^2-alpha_2)(w^2-alpha_3)(w-alpha_5))` `(w+1)/(w^5+1)=((w-alpha_1)...(w-alpha_4))/((w^2-alpha_1)....(w^2-alpha_4))` `w^2/w=((w-alpha_1)...(w-alpha_4))/((w^2-alpha_1)....(w^2-alpha_4))` option 1 is correct. |
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