Modified version of ARML 2009 Super Relay Problem 13

P(x)= x^2+Mx-1348 with roots a,b. Let Q(x) be a monic quadratic with roots (a+1),(b+1) Find the sum of the coefficients of Q(x). Vieta formulas are obvious components of the solution process. The coefficient of x for the given quadratic expression had NO influence on the answer. A monic polynomial is defined to have the constant 1 as its leading coefficient. Minnesota State University math department treats this topic thoroughly.
Read Las Vegas native FalconMaster commentary on the difficult logistics of Super Relay.
Some very tough Suffolk county math teams! They even have a math teacher's association(Jeanann Loiacono is indispensable ).
Ironically, Super Relay Problem do not bear on team standings.