If α, β are the zeros of the polynomial f (x) = x^2 + x + 1, then 1/α + 1/β = A. 1 B. – 1 C. 0 D. None of these

Question

If α, β are the zeros of the polynomial f (x) = x² + x + 1, then \(\frac{1}{\alpha}\) + \(\frac{1}{\beta}\) =

A. 1

B. – 1

C. 0

D. None of these

Answer 1

Given,

f(x) = x² + x + 1

α = a, β = b, c = c

α + β = – b/a

= – 1/1

= – 1 …….. Equ.(i)

αβ = c/a = 1 ….. Equ.(ii)

Dividing (i) from (ii)

We get,

– 1/1 = – 1

So,

1/α + 1/β = – 1