Question

if alpha and beta are the zeros of x^2-x-2, form a quadratic polynomial in x whose zeros are 2alpha+1 and 2 beta+1

Answer 1

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@Rêyaañ11

Answer 2

$from \: the \: polynomial \\ \alpha + \beta = 1 \: and \: \alpha \beta = - 2$
$sum \: of \: the \: roots \: of \: required \: polynomial \\ (2 \alpha + 1) + (2 \beta + 1) = \\ 2( \alpha + \beta ) + 2 = 4$
$product \: of \: the \: roots \: of \: required \: polynomial \\ (2 \alpha + 1) \times (2 \beta + 1) = \\ 4 \alpha \beta + 2( \alpha + \beta ) + 1= \\ 4 \times - 2+ 2 \times 1 + 1 = - 5$
$thus \: required \: polynomial \: is \\ {x}^{2} - 4x - 5$