theorem Th25: :: POLYEQ_3:25

for z, z1, z3 being Complex st z1 <> 0 & Polynom (z1,0,z3,z) = 0 holds
for s being Complex holds
( not s = - (z3 / z1) or z = (sqrt (((Re s) + (sqrt (((Re s) ^2) + ((Im s) ^2)))) / 2)) + ((sqrt (((- (Re s)) + (sqrt (((Re s) ^2) + ((Im s) ^2)))) / 2)) * <i>) or z = (- (sqrt (((Re s) + (sqrt (((Re s) ^2) + ((Im s) ^2)))) / 2))) + ((- (sqrt (((- (Re s)) + (sqrt (((Re s) ^2) + ((Im s) ^2)))) / 2))) * <i>) or z = (sqrt (((Re s) + (sqrt (((Re s) ^2) + ((Im s) ^2)))) / 2)) + ((- (sqrt (((- (Re s)) + (sqrt (((Re s) ^2) + ((Im s) ^2)))) / 2))) * <i>) or z = (- (sqrt (((Re s) + (sqrt (((Re s) ^2) + ((Im s) ^2)))) / 2))) + ((sqrt (((- (Re s)) + (sqrt (((Re s) ^2) + ((Im s) ^2)))) / 2)) * <i>) )