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

1.	If α, β are the zeroes of x2 + x + 1, then 1/α + 1/β = ……………A) 1 B) -1 C) 2 D) -2
Answer» 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 Correct option is B) -1

If α, β are the zeroes of x2 + x + 1, then 1/α + 1/β = ……………A) 1 B) -1 C) 2 D) -2

Answer»

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

Correct option is B) -1