12. Consider finding a rational function p(x) = (a + bx)/(1 + cx) that satisfies p(x;) = y; i = 1,2,3 with x,, x2, x, distinct. Does such a function p(x) exist, or are additional conditions needed to...

Extracted text: 12. Consider finding a rational function p(x) = (a + bx)/(1 + cx) that satisfies p(x;) = y; i = 1,2,3 with x,, x2, x, distinct. Does such a function p(x) exist, or are additional conditions needed to ensure existence and uniqueness of p(x)? For a general theory of rational interpolation, see Stoer and Bulirsch (1980, р. 58).