Reduce the long polynomial to the standard form of a quadratic polynomial by combining 

like terms.  You will get  5x^2 - 4x + 1.


Thus this shortened polynomial has the same roots as the polynomial Ax^2 + Bx + 1.


The fact that two polynomials of the same degree with real coefficients have the same roots
means that these polynomials have proportional coefficients 
(one common proportionality factor for two sets of coefficients).


But these polynomials have one common value  "1"  of the constant terms.


It implies that co-named coefficients in these polynomials are equal:

    A = 5,  B = -4.


So, A + B = 5 + (-4) = 1.      ANSWER

Ax^2+Bx+1 are the same as the roots of x^2 - 3x + 5 + 4x^2 - x - 4

Combine like terms:

 = 

So they are identical expressions.

Let x = 1

 = 

 = 

Edwin