No. While the sum of two qudratics cannot have a power greater than two, it could have a power of 2, 1 or 0.
x2 + 1 is one quadratic
(2-x)(2+x) is another quadratic.
Their sum is 1, a constant (power = 0).
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Such a sum is always rational.
Yes.
The sum of two consecutive integers will always be an odd number.
The sum of two polynomials is always a polynomial. Therefore, it follows that the sum of more than two polynomials is also a polynomial.
11 and 11. In general, you can write an equation (or two equations), and solve with the quadratic formula, to solve this type of questions.