Question

correct explanation... I'll gave them brainlist
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Answer 1

SOLUTION :

Process 1

$\sf \: f(x)= {x}^{2} - x( \alpha + \beta ) + \alpha \beta$

We know for all quadratic equation,

$\sf {x}^{2} -( sum \: of \: roots)x + product \: of \: roots = 0$

$\sf \boxed{ \mathfrak{Hance \: the \: roots \: are \: \alpha \: and \: \beta }}$

Process 2

$\sf {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$

$\to \sf \: {x}^{2} - \alpha x - \beta x + \alpha \beta = 0$

$\to \sf \:x (x - \alpha) - \beta (x - \alpha ) = 0$

$\to \sf \: (x - \alpha )(x - \beta ) = 0$

$\to\: \: \: \: \boxed{ \mathfrak{x = \alpha \: \: \: \: \: or \: \: \: \: \: \: x = \beta }}$