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  • Solve this problem - Complex numbers and quadratic equations - JEE Main-4

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

 

Answers (1)

best_answer

\\*\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

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divya.saini

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