Question

if alpha beta are the zeroes of f(x) =x^2 +x+1 than find 1/alpha + 1/beta

Answer 1

Answer :

The given polynomial is

f (x) = x² + x + 1

Since, α and β are zeroes of f (x), we get

α + β = - 1

and

αβ = 1

∴ 1/α + 1/β

= (β + α)/(αβ)

= ( - 1)/1

= - 1

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Answer 2

Hi there!

Given poly. :- f (x) = x² + x + 1

Here, a = 1, b = 1 n' c = 1

→ Sum of Zeroes = α + β = -b / a = - 1

→ Product od Zeroes = α.β = c / a = 1

ATQ,

∴ 1 / α + 1 / β

= α + β / α.β

= -1 / 1

= -1

Hence, The required answer is = - 1

Hope it helps! :)