Question

answer these questions ​

Answer 1

Answer:

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Step-by-step explanation:

$Q.8 \\ to \: find = \\ quadratic \: equation \\ \\ so \: for \: a \: certain \: quadratic \: equation \\ let \: its \: two \: roots \: be \: \alpha \: and \: \beta \\ \\ so \: according \: to \: first \: condition \\ \alpha + \beta = 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ (1) \\ \\ according \: to \: second \: condition \\ \alpha {}^{2} + \beta {}^{2} = 25 \: \: \: \: \: \ \: \: (2) \\ \\ so \: we \: know \: that \\ \alpha {}^{2} + \beta {}^{2} = ( \alpha + \beta ) {}^{2} - 2 \alpha \beta \\ \\ from \: (1) \: and \: (2) \\ we \: get \\ \\ 25 = (7) {}^{2} - 2 \alpha \beta \\ 25 = 49 - 2 \alpha \beta \\ 2 \alpha \beta = 24 \\ \\ ie \: \: \alpha \beta = 12$

$so \: we \: know \: that \\ general \: equation \: (in \: terms \: of \: \alpha \: and \: \beta ) \: \\ of \: quadratic \: equation \: is \: given \: by \\ x {}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ x {}^{2} - (7)x + 12 = 0 \\ \\ \: x {}^{2} - 7x + 12 = 0 \\ \\ hence \: required \: equation \: is \: x {}^{2} - 7x + 12 = 0$