Question

find the equation whose roots are 3times the roots of xcube+2xsquare-4x+1=0
plz answer me above question​

Answer 1

Step-by-step explanation:

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Asked on December 27, 2019 by

Dumpa Chaubey

The cubic equation whose roots are thrice to each of the roots of x

3

+2x

2

−4x+1=0 is

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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