yeah it is
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The proposition is not true.pi and -pi are both irrational. But their sum, = 0, is rational.
Not always. For example: sqrt(2)+(-sqrt(2))=0 which is not irrational.
Any number multiplied by zero will always give the result of zero.
Such a sum is always rational.
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).