question_answer

Let \[\alpha ,\beta \] and \[\gamma \] be the roots of the equation \[{{x}^{3}}-{{x}^{2}}+3x+1=0\]. Then the value of  is equal to

A) \[-10\]                

B) \[-8\]   

C) \[7\]                        

D) \[9\]

Correct Answer: B

Solution :

[b] Applying \[{{C}_{3}}\to {{C}_{3}}-2{{C}_{1}}-2{{C}_{2}},\] we get \[=(\alpha +\beta +\gamma )({{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}}-\alpha \beta -\beta \gamma -\gamma \alpha )\] \[=(\alpha +\beta +\gamma )({{(\alpha +\beta +\gamma )}^{2}}-3(\alpha \beta +\beta \gamma +\gamma \alpha ))\] \[=1\times ({{1}^{2}}-3\times (3))\] \[=-8\]