question_answer

If \[{{\cos }^{-1}}(p+iq)=u+iv,\]then the equation with the roots \[{{\cos }^{2}}u\]and \[{{\cos }^{2}}v\]

A)  \[{{x}^{2}}-x\,\,({{p}^{2}}+{{q}^{2}})+{{p}^{2}}=0\]

B)  \[{{x}^{2}}-x\,\,({{p}^{2}}+{{q}^{2}}+1)+1=0\]

C)  \[{{x}^{2}}+x\,\,({{p}^{2}}+{{q}^{2}}+1)+1=0\]

D)  \[{{x}^{2}}-x\,\,({{p}^{2}}+{{q}^{2}}+1)+{{p}^{2}}=0\]

E)  None of these