If one of the zeroes of a quadratic polynomial of the form $x^2+ax+b$ is the negative of the other, then which of the following is correct?

If one of the zeros of the equation is negative of the other, then the roots will be $m$ and $-m$. 

Hence, the sum of roots $=m-m=0$ 

The sum of roots, $a=0$ 

Thus there will be no linear involved in the term in the equation. 

Also, the constant term, b = product of the zeroes $=-m^2$, will be negative. 

Hence, the quadratic polynomial has no linear term and the constant term is negative.