Question

If α, β are the zeros of the polynomial x2

+x+1,then Find the value of



+





.​

Answer 1

$x^2+x+1$

$Two \: zeroes \: of \: \\ polynomial \: are \: \alpha,\beta.$

$\frac{1}{\alpha}+\frac{1}{\beta}$

$\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\beta+\alpha}{\alpha\beta}$

$x^2-(\alpha+\beta)x+\alpha\ \times \beta$

α+β=−1

α×β=1

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

$Hence, \frac{1}{\alpha}+\frac{1}{\beta}==-1$