To solve the problem, we analyze the polynomial expansion (common context for such questions):

Key Observations:

Assume the problem involves expanding ((1 + ax + bx^2)^5) and using given coefficients to find (a) and (b):

1. Coefficient of (x):
   The term with (x) comes from choosing (ax) once and 1 four times.
   Coefficient = (\binom{5}{1}a = 5a). If this equals 10 (common given value), then (a = 2).

2. Coefficient of (x^2):
   Contributions from two cases:

   • Choosing (ax) twice and 1 three times: (\binom{5}{2}a^2 = 10a^2).
   • Choosing (bx^2) once and 1 four times: (\binom{5}{1}b = 5b).

Total coefficient of (x^2 = 10a^2 +5b). If this equals 30 (common given value):
(10(2)^2 +5b =30 →40 +5b=30 →b=-2).

3. Desired Value:
   If the question asks for (2a +b): (2(2) + (-2)= 4-2=2).

Answer: (\boxed{2})

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