If \[a=\cos (2\pi /7)+i\,\sin (2\pi /7),\] then the quadratic equation whose roots are \[\alpha =a+{{a}^{2}}+{{a}^{4}}\] and \[\beta ={{a}^{3}}+{{a}^{5}}+{{a}^{6}}\] is [RPET 2000]

If \[a=\cos (2\pi /7)+i\,\sin (2\pi /7),\] then the quadratic equation

1.	If \[a=\cos (2\pi /7)+i\,\sin (2\pi /7),\] then the quadratic equation whose roots are \[\alpha =a+{{a}^{2}}+{{a}^{4}}\] and \[\beta ={{a}^{3}}+{{a}^{5}}+{{a}^{6}}\] is [RPET 2000]
A.	\[{{x}^{2}}-x+2=0\]
B.	\[{{x}^{2}}+x-2=0\]
C.	\[{{x}^{2}}-x-2=0\]
D.	\[{{x}^{2}}+x+2=0\]
Answer» E.