If the least and the largest real values of α , for which the equation z+αz−1+2i=0z∈C and i=−1 has a solution, are p and q respectively, then 4p2+q2 is equal to_______.

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Detailed Solution

x+iy+αx−12+y2+2i=0⇒y+2=0 & x+αx−12+y2=0It gives y=−2 , x2=α2x−2x+1+4α2=x2x2−2x+5⇒ α2∈0,54Therefore, 4αmax2+αmin2=40+54=5