Interesting equation
Source: Canada 2001
March 4, 2006
quadraticsalgebrapolynomialfunction
Problem Statement
Randy: "Hi Rachel, that's an interesting quadratic equation you have written down. What are its roots?''
Rachel: "The roots are two positive integers. One of the roots is my age, and the other root is the age of my younger brother, Jimmy.''
Randy: "That is very neat! Let me see if I can figure out how old you and Jimmy are. That shouldn't be too difficult since all of your coefficients are integers. By the way, I notice that the sum of the three coefficients is a prime number.''
Rachel: "Interesting. Now figure out how old I am.''
Randy: "Instead, I will guess your age and substitute it for in your quadratic equation darn, that gives me , and not .''
Rachel: "Oh, leave me alone!''
(1) Prove that Jimmy is two years old.
(2) Determine Rachel's age.