Question

12. The quadratic equations
having 1/a,1/ß ​

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \: for \: a \: certain \: quadratic \: equation \\ its \: roots \: are \: 1/ \alpha \: and \: 1/ \beta$

$so \: we \: know \: that \\ general \: formula \: of \: quadratic \: equation \: (in \: terms \: of \: \alpha \: and \: \beta ) \: is \: given \: by \\ x {}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ wherein \: \alpha \: and \: \beta \: are \: its \: two \: roots$

$so \: hence \\ x {}^{2} -( 1/ \alpha + 1/ \beta )x + 1/ \alpha \times 1/ \beta = 0 \\ x {}^{2} - ( \alpha + \beta / \alpha \beta )x + 1/ \alpha \beta = 0 \\ x {}^{2} - ( \alpha + \beta )x + 1/ \alpha \beta = 0 \\ dividing \: and \: multiplying \: throughout \: by \: \alpha \beta \\ we \: get \\ \\ \alpha \beta .x {}^{2} - ( \alpha + \beta ) + 1 = 0$

$hence \: the \: quadratic \: equation \: whose \: roots \: are \: 1/ \alpha \: and \: 1/ \beta \: is \\ \alpha \beta .x {}^{2} - ( \alpha + \beta )x + 1 = 0 \\ ie \: option \: \: (D) \: is \: ryt$