Problem with Left-sided Polynomials

Until today I believed that the theory of left-sided polynomials in quaternion algebra is consistent, although it cannot have applications in related theories. Today I realized that this theory contains a serious contradiction. Nivem theorem asserts that left-sided polynomial of power n has n roots. However, polynomial $$x^2-(i+j)x+k$$ has only root \(x=j\). Even we assume that this root has multiplicity 2, then we get equality $$(x-j)(x-j)=x^2-jx-xj+1$$ If we assume multiplication of left-sided polynomials, then we get equality $$(x-j)(x-j)=x^2-2jx+1$$ It is evident that left side of this equality is different from expression of polynomial.