Question

α,β are the roots of the quadratic equation X^2 + X + 1=0, then 1/α+1/β

Answer 1

Answer:

Step by step explanation:

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Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore \frac{1}{\alpha}+\frac{1}{\beta}=-1}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about α,β are the roots of the quadratic equation X^2 + X + 1=0.

• We have to find 1/α+1/β.

$\underline \bold{Given : } \\ \implies \alpha \: \: and \: \: \beta \in ({x}^{2} + x + 1 = 0) \\ \\ \underline \bold{To \: Find : } \\ \implies \frac{1}{ \alpha } + \frac{1}{ \beta } = ?$

• According to given question :

$\implies{x}^{2} + x + 1 = 0 \\ \bold{a = 1 \: \: \: \: b = 1 \: \: \: \: c = 1} \\ \\ \bold{sum \: of \: zeroes : } \\ \implies\alpha + \beta = \frac{ - b}{a} \\ \\ \implies \alpha + \beta = \frac{ - 1}{1} \\ \\ \bold{product \: of \: zeroes : } \\ \implies \alpha \times \beta = \frac{c}{a} \\ \\ \implies \alpha \beta = \frac{1}{1} \\ \\ \bold{for \: finding \: value : } \\ \implies \frac{1}{ \alpha } + \frac{1}{ \beta } \\ \\ \implies \frac{ \beta + \alpha }{ \alpha \beta } \\ \\ \implies \frac{ \alpha + \beta }{ \alpha \beta } \\ \\ \implies \frac{ \frac{ - 1}{1} }{ \frac{1}{1} } \\ \\ \bold{\implies - 1}$