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If `alpha ,beta, gamma ` are the roots of ` x^3-3ax+b=0`
prove that `sum (alpha-beta)(alpha-gamma)=9a`.

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`alpha ,beta, gamma ` are the roots of ` x^3-3ax+b=0`
`rArr alpha+beta+gamma=0`,`alphabeta+betagamma+gammaalpha=-3a`,` alphabetagamma=-b`
`sum(alpha-beta)(alpha-gamma)``=sum [alpha^2-alpha(beta+gamma)+betagamma]``=sum[alpha^2+alpha^2+betagamma]`
`=2(alpha^2+beta^2+gamma^2)+(betagamma+gammaalpha+alphabeta)`
`2(alpha+beta+gamma)^2-4(alphabeta+betagamma+gammaalpha)+(alphabeta+betagamma+gammaalpha)`
=0-4(-3a)+(-3a) =9a.
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-THEORY OF EQUATIONS -EXERCISE -4(a)
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