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) | ||
\[10-a=a-6\] | ||
\[a=8\] | ||
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