(A)
Let p(x) = x2+ax+b
Now, product of zeroes = constant termcoefficient of x2
Let α and β be the zeroes of p (x)
∴ product of zeroes (αβ)=b1
⇒ αβ = b
Given that, one of the zeroes of a quadratic polynomial p(x) is negative of the other
∴ αβ<0
So, b<0
Hence, b should be negative
Put a = 0, then, p(x)=x2+b=0
⇒ x2=−b
⇒ a=0
∴ f(x)=x2+b , which cannot be linear
And product of zeroes = α(−α)=b
⇒ −a2=b
Which is possible when b < 0
Hence, it has no linear term and the constant term is negative.