If α and β are the zeroes of the polynomial $$x^2+x+1$$​ then the value of $$\frac{1}{α}+\frac{1}{β}$$​ will be:

Correct option is C

Given:

The polynomial equation is:

x$$^2$$​ + x + 1 = 0

The sum and product of the roots (zeroes) α and β are

Sum of roots: α + β = $$-\frac{b}{a} = -\frac{1}{1}$$​ = -1

Product of roots: αβ = $$\frac{c}{a} = \frac{1}{1}$$​ = 1

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

Solution:

$$\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha \beta}\\ \ \\ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{-1}{1} = -1\\ \ \\\boxed{-1}$$​