A) 6
B) 8
C) 4
D) 2
Correct Answer: B
Solution :
| Let \[{{N}^{r}}=f(x)={{x}^{3}}+(a-10){{x}^{2}}-x-a-6=0\] has roots \[\alpha ,\beta ,\gamma \] |
| & \[{{D}^{r}}=g(x)={{x}^{3}}+(a-6){{x}^{2}}-x+a-10=0\] has roots \[\alpha ,\beta ,\rho \] |
| \[\therefore \,\,f(x)-g(x)=-\,4{{x}^{2}}+4=0\Rightarrow x=\pm \,\,1\] |
| \[\therefore \,\,\alpha +\beta =0,\]\[\alpha \beta =-\,1\] |
| \[\therefore \,\,\alpha +\beta +\gamma =-\,(a-10)=10-a\] |
| \[\Rightarrow \gamma =10-a\] | ... (i) | |
| \[\alpha \beta \gamma =6-a\] | ||
| \[\Rightarrow \gamma =a-6\] | .... (ii) | |
| From (i) & (ii) | ||
| \[10-a=a-6\] | ||
| \[a=8\] | ||
You need to login to perform this action.
You will be redirected in
3 sec
