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Question

If α,β and γ are the roots of x3-2x+1=0 then the value of 1α+β-γ is


A

-12

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B

-1

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C

0

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D

12

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Solution

The correct option is B

-1


Explanation for the correct option:

Step 1. Find the value of 1α+β-γ:

Given, α,β and γ are the roots of x3-2x+1=0

x3xx+1=0

x(x21)(x1)=0

x=1,x2+x1=0

α=1,β=-1+52,γ=-1-52

Step 2. Find the value of α,αβ,αβγ:

α=α+β+γ=1+-1+52+-1-52=0

αβ=αβ+βγ+γα=1×-1+52+-1+52×-1-52+-1-52×1=-82=-4

αβγ=1×-1+52×-1-52=-42=-2

Step 3 . Put the values of α,αβ,αβγ in 1α+β-γ, we get

1α+βγ=1-γγ=1-2γ=-121α+1β+1γ=-12αβ+βγ+γααβγ=-12×αβαβγ=-12×-4-2=-1

Hence, Option ‘B’ is Correct.


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