Question

If α, β are the zeroes of x² + x + 1, then 1/α + 1/β = ……………

A) 1 

B) -1 

C) 2 

D) -2

Answer 1

Correct option is (B) -1

Given that \(\alpha\;and\;\beta\) are zeros of \(x^2+x+1.\)

\(\therefore\) Sum of roots \(=\frac{\text{-coefficient of x}}{\text{coefficient of }x^2}=\frac{-1}1\) = -1

\(\Rightarrow\) \(\alpha+\beta\) = -1

And product of zeros \(=\frac{\text{constant term}}{\text{coefficient of }x^2}=\frac11\) = 1

\(\Rightarrow\) \(\alpha\beta=1\)

Now, \(\frac{\alpha+\beta}{\alpha\beta}=\frac{-1}1\) = -1

\(\Rightarrow\) \(\frac1\alpha+\frac1\beta\) = -1

Answer 2

Correct option is B) -1