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If alpha,betaa n dgamma are the roots of...

If `alpha,betaa n dgamma` are the roots of `x^2+8=0` then find the equation whose roots are `alpha^2,beta^2a n dgamma^2` .

Text Solution

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Let y ` = x ^(2 ) . Then x = sqrt(y)`
`therefore a^(3) + 8 = 0 rArr y^(3//2) + 8 = 0`
or `y^(3) = 64 or y^(3) - 64 = 0`
thus, the equation having roots `alpha ^(2) , beta^(2) and gamma^(2) is x^(3) - 64 = 0` .
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