Question

Find the equation whose roots are 2 times the roots of

3 2 x 2x 4x 1 0​

Answer 1

Answer:

Given equation is x

3

+2x

2

−4x+1=0

Let α,β and γ be the roots of the given equation

∴α+β+γ=−2,αβ+βγ+γα=−4 and αβγ=−1

Let the required cubic equation has the roots 3α,3β and 3γ.

⇒3α+3β+3γ=−6,

3α⋅3β+3β+3γ+3γ⋅3α=36

and 3α⋅3β⋅3γ=−27

∴ required equation is

x

3

−(−6)x

2

+(−36)x−(−27)=0

⇒x

3

+6x

2

−36x+27=0

Step-by-step explanation:

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