If one of the zeroes of a quadratic polynomial of the form \(x^2+ax+b\) is the negative of the other, then it
has no linear term and the constant term is negative
has no linear term and the constant term is positive
can have a linear term but the constant term is negative
can have a linear term but the constant term is positive
Step 1: Assume the zeroes.
Let the two zeroes be \(r\) and \(-r\).
Step 2: Form the quadratic polynomial.
If \(r\) and \(-r\) are the zeroes, then the polynomial is
\((x - r)(x + r) = x^2 - r^2\).
Step 3: Compare with the given form.
The polynomial becomes \(x^2 + ax + b\).
Here, the coefficient of \(x\) is \(a = 0\), so there is no linear term.
The constant term is \(b = -r^2\).
Step 4: Sign of the constant term.
Since \(r^2 \geq 0\) for all real \(r\),
\(b = -r^2 \leq 0\).
Therefore, the constant term is negative (unless \(r = 0\), in which case the polynomial is just \(x^2\)).
Conclusion: The polynomial has no linear term and the constant term is negative. So the correct option is (A).