Question

If
$\alpha + \beta$
are the zeroes of the quadratic polynomial . Such that
$\alpha + \beta = 24$
and
$\alpha - \beta = 8$
Find the quadratic polynomial having
$\alpha$
and
$\beta$
as it's zeroes

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Answer 1

Answer:

$\alpha + \beta = 24 \\ \alpha - \beta = 8 \\ adding \: both \: the \: equation \\ 2 \alpha = 32 \\ \alpha = 16 \\ \beta = 24 - 16 = 8 \\ now \\ \alpha \beta = 128 \\ quadratic \: equation \: is \:$

${x}^{2} - (\alpha + \beta )x + \alpha \beta \\ {x}^{2} - 24x + 128$