If α and β are the roots of the polynomial f(x) = x2 + x + 1 then the value of \(\rm \frac{1}{\alpha}+\frac{1}{\beta}\) will be :

Concept -

If α and β are the roots of the polynomial f(x) = ax2 + bx + c then

sum of roots = -b/a

product of roots = c/a

Explanation -

Now we have -

If α and β are the roots of the polynomial f(x) = x2 + x + 1

then α + β = -1 .....(i)

and α.β = 1...... (ii)

Now we want to find the value of  \(\rm \frac{1}{\alpha}+\frac{1}{\beta}\)

= \(\frac{\alpha+\beta}{\alpha.\beta}\)

Now put the value of equation (i) and (ii) we get -

= -1/1 = -1

Hence option (3) is true.