Question

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Answer 1

Answer:-

This is the required solution.

Given,

$\sf p(x) = {x}^{2} - 5x + 8$

Here,

$\sf a = 1$

$\sf b = - 5$

$\sf c= 8$

Now,

remember that,

$\boxed{ \sf \large \alpha + \beta = \frac{ - b}{a} }$

And,

$\boxed{ \sf \large \alpha \beta = \frac{c}{a} }$

So,

Here,

$\sf \alpha + \beta = \frac{ - b}{a} = \frac{ - ( - 5)}{1} = 5$

And,

$\sf \alpha \beta = \frac{c}{a} = \frac{8}{1} = 8$

So,

$\sf \frac{1}{ \alpha } + \frac{1}{ \beta }$

$\sf = \frac{ \beta + \alpha }{ \alpha \beta }$

$\sf = \frac{5}{8}$

Hence,

$\boxed {\sf \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{5}{8} }$

Answer 2

Answer:

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