A) \[-2\]
B) \[-1\]
C) \[0\]
D) \[1\]
Correct Answer: C
Solution :
Given \[\operatorname{x}={{\omega }^{2}}-\omega -2\] \[\Rightarrow \,\,\,x+2={{\omega }^{2}}-\omega \] On squaring both sides, we get \[\Rightarrow \,\,\,{{(x+2)}^{2}}=\,\,{{\left( {{\omega }^{2}}-\omega \right)}^{2}}\] \[\Rightarrow \,\,\,\,{{\operatorname{x}}^{2}} + 4x + 4 = {{\omega }^{4}} + {{\omega }^{2}}- 2 {{\omega }^{3}}\] Add 3 on both side \[\Rightarrow \,\,{{\operatorname{x}}^{2}}+4x+4+3=\omega +{{\omega }^{2}}-2+3\,\,\,\left( \because \,\,{{\omega }^{3}}=1 \right)\] \[{{\operatorname{x}}^{2}} + 4x + 7 = 1 + \omega + {{\omega }^{2}}\] \[\Rightarrow \,\,\,{{\operatorname{x}}^{2}} +4x\times 4-7 =0\,\,\left( \because \,\, 1+\omega +{{\omega }^{2}} =0 \right)\]
You need to login to perform this action.
You will be redirected in
3 sec
