Question

if alpha and beta are zeroes of p(x) =x2

Answer 1

Hey user

Here is your answer :-

$p(x) = {x}^{2} + x + 1 \\ \\ \alpha \: \: and \: \: \beta \: \: are \: the \: roots \: of \: given \: equation \: \\ \\ comparing \: the \: equation \: with \: standard \: form \\ \\ here \: a = 1 \: \: b = 1 \: \: c = 1 \\ \\ we \: know \: that \: \\ \\ \alpha + \beta = \frac{ - b }{a} = - 1\\ \\ \alpha \beta = \frac{c}{a} = 1 \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta } \\ \\ = - \frac{ - 1}{1} \\ \\ = - 1$

Thank you .