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Question
If α,β,γ are the roots of the equation x3−3x+11=0, then the equation whose roots are (α+β),(β+γ) and (γ+α) is :
If α,β,γ are the roots of the equation x3−3x+11=0, then the equation whose roots are (α+β),(β+γ) and (γ+α) is :
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Solution
The correct option is D x3−3x−11=0
We have, α+β+γ=0
∴β+γ=−α,γ+α=−β and α+β=−γ.
∴ The equation whose roots are −α,−β,−γ can be obtained by replacing x by - x in the given equation.
Therefore the required equation is:
(−x)3−3(−x)+11=0
Or x3−3x−11=0
We have, α+β+γ=0
∴β+γ=−α,γ+α=−β and α+β=−γ.
∴ The equation whose roots are −α,−β,−γ can be obtained by replacing x by - x in the given equation.
Therefore the required equation is:
(−x)3−3(−x)+11=0
Or x3−3x−11=0
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