Question

alpha + beta are the roots of x square + X + 1 then find the value of one upon alpha + 1 upon beta​

Answer 1

Given -

$\alpha \: and \: \beta \: are \: \: the \: \: roots \: of \: {x}^{2} + x + 1$

To find -

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

Solution -

Here,

a=1

b=1

c=1

p(x) =x²+1+x

Sum of zeroes

$\alpha + \beta = \frac{ - b}{a} = - 1.....1)$

Product of zeroes

$\alpha \beta = \frac{c}{a} = 1.....2)$

Now,

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

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

$= \frac{ - 1}{1} (by \: 1 \: and \: 2)$

$= - 1$