Question

if alpha beta gamma are the roots of 9 x cube minus 7 x + 6 = 0 then alpha beta gamma is​

Answer 1

Explanation:

$given \: equation \: is \: 9 {x}^{3}-7x + 6 = 0 \\ \: on \: comparing \: with \: ax^{3}+bx^{2} + cx + d = 0 \\ \: we \: have \: a = 9 \: ,\: \: b = 0 \: , \: \: \: c = - 7 \: and \: \: \: d = 6 \\ \: if \: \alpha, \: \beta , \: \gamma ,\: are \: te \: roots \: then \\ \: sum \: of \: the \: roots </p><p>= \alpha + \beta + \gamma </p><p> = - \frac{b}{a} </p><p>= - \frac{0}{9} = 0 </p><p>\\ \: product \: of \: the \: roots \: </p><p> = \alpha \beta \gamma </p><p> = - \frac{d}{a}</p><p> = - \frac{6}{9} </p><p> = - \frac{2}{3}$

Answer 2

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