A PROOF BY ELEMENTARY METHODS, WITHOUT COMPLEX QUANTITIES, THAT EVERY ALGEBRAIC FUNCTION (WITH REAL COEFFICIENTS) HAS FACTORS OF THE FORM (<i>x</i><sup>2</sup>-<i>px</i>+<i>q</i>(<i>p, q</i>, REAL) AND HENCE, EVERY ALGEBRAIC EQUATION WITH COEFFICIENTS REAL OR IMAGINARY, HAS REAL OR IMAGINARY ROOTS EQUAL IN NUMBER TO THE DEGREE OF THE EQUATION
Transactions of the Royal Society of South Africa