Question

$if \: \alpha \: and \: \beta \: are \: zeroes \: of \: the \: polynomial \: 6x {}^{2} - 3 - 7x \: find \: \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha }$
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Answer 1

Answer:

6x² - 7x - 3

$\alpha + \beta = \frac{ - b}{a} \\ \\ \alpha + \beta = \frac{7}{6}$

And,

$\alpha \beta = \frac{c}{a} \\ \\ \alpha \beta = \frac{ - 3}{6} = \frac{ - 1}{2}$

Now,

$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } \\ \\ \frac{ \alpha + \beta }{ \alpha \beta } \\ \\ \frac{7}{6} \div (\frac{ - 1}{2} ) \\ \\ \frac{7}{6} \times ( - 2) \\ \\ \frac{ - 7}{3}$

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