The equation x a + x b + x = x c + x d + 1 considered in this paper is a particular equiponderate equation. The number and location of the roots (w.r.t. x = 1) of this equation are determined in case ( a , b , c , d ) ∈ ] 0 , 1 [ 4 . Based on these results, it is shown that any weight quadruplet, a basic tool in fuzzy preference modelling, admits an interesting expression in terms of Frank t-norms with reciprocal parameters.