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Question

If α,β and γ are the roots of x3+2x2-3x-1=0, then α-2+β-2+γ-2 is equal to


A

12

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B

13

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C

14

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D

15

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Solution

The correct option is B

13


Explanation for the correct option:

Find the value of α-2+β-2+γ-2:

Given, α,β and γ are the roots of x3+2x2-3x-1=0

α=2,αβ=3,αβγ=1

As we know,

1α=(αβ)2(αβγ)2=(αβ)22(αβγ)(α)(αβγ)2=(-3)22(-2)1=9+4=13

The value of α-2+β-2+γ-2 is 13

Hence, Option ‘B’ is Correct.


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