Question

. If α ,β are the zeroes of f(x) = x^2+ x+1 then find 1/( α)+ 1/β.



do it step by step

Answer 1

=1/alpha + 1/ beta
=beta+alpha/alpha.beta
=-b/a/c/a
=-b/c
=-1

hope it help you

Answer 2

Given that Alpha and Beta are the zeroes of the polynomial f(x) x^2 + x + 1.

We know that sum of zeroes (alpha + beta) = -b/a

                                                                       = -1/1

                                                                       = -1.


We know that product of zeroes (alpha * beta) = c/a

                                                                              = 1/1

                                                                              = 1.


Now,

1/alpha + 1/beta = (alpha + beta)/(alpha * beta)

                           = (-1)/(1)

                           = -1.


Therefore 1/alpha + 1/beta = -1.


Hope this helps!