In Years 9 and 10 of secondary schooling students are typically introduced to quadratic expressions and functions and related modelling, algebra, and graphing. This includes work on the expansion and factorisation of quadratic expressions (typically with integer values of coefficients), graphing quadratic functions, finding the roots of quadratic equations and relating these to horizontal axis intercepts of corresponding graphs. Classroom experience suggests that students find Vieta's formulas named after the French mathematician Franciscus Vieta (in French, Francois Viete; 1540-1603), to be a very appealing way of finding the roots x[subscript 1], x[subscript 2] of a quadratic equation ax[superscript 2] + bx + c with real coefficients a [not equal to] 0, b and c and nonnegative discriminant. That is particularly true when the roots x[subscript 1] and x[subscript 2] are positive integers. In this article, the author focuses on Vieta's formulas and the determination of a set of positive integers by their sum and product. (Contains 3 tables and 4 figures.)