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Q.

If α,β,γ are the roots of x3 + 2x2  4x 3= 0 then the equation whose roots are α3,β3,γ3 is

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a

x3+6x2-36x-81=0

b

9x3+6x2+4x+1=0

c

x3-6x2+36x+81=0

d

9x3+6x2-4x-1=0

answer is B.

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Detailed Solution

Letα,β,γarerootsoff(x)=x3+2x24x3=0Thentheequationwhoserootsareα3,β3,γ3isf(3x)=0(3x)3+2(3x)24(3x)3=027x3+18x212x3=09x3+6x24x1=0

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If α,β,γ are the roots of x3 + 2x2 – 4x –3= 0 then the equation whose roots are α3,β3,γ3 is