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If alpha, beta, gamma are the roots of t...

If `alpha, beta, gamma` are the roots of the equation `x^3+ qx +r =0`then find the equation whose roots are (a) `alpha+beta, beta+gamma, gamma+alpha` (b) `alpha beta, beta gamma, gamma alpha`

Text Solution

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a)`alpha+beta+gamma=0`
`alphabeta+betagamma+gammaalpha=q`
`alphabetagamma=-r`
`2(alpha+beta+gamma)=0=b`
`x^3-bx^2+cx-d=0`
`C=alphabeta+alphagamma+beta^2+betagamma+betaalpha+gamma^2+gammaalpha+alphabeta+alpha^2+alphabeta`
`c=(alpha+beta+gamma)^2+(alphabeta+gammabeta+alphagamma)`
`c=q`
...
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