How to transfer the solve data to another function



How to transfer the solve data to another function?

Q: f(x)=x^2+ax+b,f(1)=10,f(2)=5, solve f(x)=?
I want to transfer the data of the solve([eq1,eq2]) to F(a,b) directly,
don't input F(-8,17) by myself.
   
 How Can I to do? 

f(x):=x^2+a*x+b;
F(a,b):=f(x);
eq1:f(1)=10;
eq2:f(2)=5;
solve([eq1,eq2]);
F(-8,17);

(%o34) f(x):=x^2+a*x+b
(%o35) F(a,b):=f(x)
(%o36) b+a+1=10
(%o37) b+2*a+4=5
(%o38) [[b=17,a=-8]]
(%o39) x^2-8*x+17

 		 	   		  
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