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1 solution
The given equation reduces to f(x)= x^4+2x^3+3x^2+2x- 48=0; The integral values of x that will satisfy the equation should be among the factors of constant term - 48. Since, 48= 2^4*3 and all factors 48 are also the factors of - 48 and x=2 and x=-3 satisfy the equation f(x)=0, hence, f(x) can be written as f(x)= (x-2)(x+3)(x^2+x+8). The quadratic factor x^2+x+8 yields imaginary roots. Thus, sum of real roots=2+(-3)= -1