Hunduma LegesseLeyla Abdulkadir2025-08-172025-08-172024-10https://etd.aau.edu.et/handle/123456789/6925In this thesis, we show that the critical curve of the quadrinomial Pb(z) = bzk + 1 k􀀀1 zk􀀀1 + 1 n zn + kb n􀀀1 zn􀀀1 is the part of the unit circle. Moreover, we prove that there are at most two singular zeros for the quadrinomial Pb(z) = bzk+ 1 k􀀀1 zk􀀀1+ 1 n zn+ kb n􀀀1 zn􀀀1 we are considering.en-USAnalytic FunctionsHarmonic PolynomialsHarmonic QuadrinomialsSense PreservingSense ReversingCritical CurvesZerosSingularand Nonsingular ZerosThesis