# If $\alpha ,\beta ,\gamma$ are roots of $x^{3}-x^{2}-1=0$ then $\frac{\alpha +1}{\alpha }+\frac{\beta +1}{\beta }+\frac{\gamma +1}{\gamma }$ equals Option 1) 2 Option 2) 3 Option 3) 4 Option 4) 5

D Divya Saini

$\\*\alpha +\beta +\gamma =1\\*\alpha \beta +\beta \gamma +\gamma \alpha =0\; ;\alpha \beta \gamma =1\\*\frac{\alpha +1}{\alpha }+\frac{\beta +1}{\beta }+\frac{\gamma +1}{\gamma }=1+\frac{1}{\alpha }+1+\frac{1}{\beta }+1+\frac{1}{\gamma }=3+\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }\\*3+\frac{\alpha \beta +\beta \gamma +\gamma \alpha }{\alpha \beta \gamma }=3+\frac{0}{1}=3$

Sum of product of pair of roots in cubic equation -

$\alpha \beta +\beta \gamma +\gamma \alpha = \frac{c}{a}$

- wherein

$ax^{3}+bx^{2}+cx+d= 0$

is the cubic equation

Option 1)

2

This is incorrect

Option 2)

3

This is correct

Option 3)

4

This is incorrect

Option 4)

5

This is incorrect

Exams
Articles
Questions