Question

If α, β are the zeros of the polynomial f(x) = x² + x + 1, then \[\frac{1}{\alpha} + \frac{1}{\beta} =\]

विकल्प

• 1

• -1

• 0

• None of these

Answer 1

Since `alpha` and  ß  are the zeros of the quadratic polynomial f(x) = x² + x + 1,

`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`

`= (-1)/1=1`

`alpha + ß = (\text{constat term})/(text{coefficient of} x^2)`

`= 1/1=1`

we have 

`= 1/alpha+ 1/ ß`

` (ß +alpha)/(alpha ß)`

`=-1/1`

`=-1`

The value of  `1/alpha + 1/ß ` is -1

Hence, the correct choice is  (b).