Question

If alpha and beta are the zeroes of polynomial xsquare-2x-8 then form polynomial whose zeroes are 3alpha and 3beta

Answer 1

$from \: the \: polynomial \\ \alpha + \beta = 2 \: and \: \alpha \beta = - 8$
$sum \: of \: the \: roots \: of \: new \: equation \\ 3 \alpha + 3 \beta = 3 \times 2 = 6$
$product\: of \: the \: roots \: of \: new \: equation \\ 3 \alpha \times 3 \beta = 9\times \alpha \beta = - 72$
$thus \: required \: polynomial \: is \\ {x}^{2} - 6x - 72$