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The quantum analogue of Bernstein operators B m , q reproduce the linear polynomials which are therefore eigenfunctions corresponding to the eigenvalue 1 , ∀ q > 0 . In this article the rest of eigenstructure of q-Bernstein operators and the distinct behaviour of zeros of eigenfunctions for cases (i) 1 > q > 0 , and (ii) q > 1 are discussed. Graphical analysis for some eigenfunctions and their roots are presented with the help of MATLAB. Also, matrix representation for diagonalisation of q-Bernstein operators is discussed. [ABSTRACT FROM AUTHOR]