Problem:
Quadratic polynomials P(x) and Q(x) have leading coefficients 2 and −2 , respectively. The graphs of both polynomials pass through the two points (16,54) and (20,53). Find P(0)+Q(0).
Solution:
Let P(x)=2x2+ax+b and Q(x)=−2x2+cx+d.
From here we can solve for a,b,c, and d.
16a+b=−45820a+b=−74716c+d=56620c+d=853
Solving gives us b=698 and d=−582.
P(0)+Q(0)=b+d=116.
The problems on this page are the property of the MAA's American Mathematics Competitions