If one of the zeroes of a quadratic polynomial of the form of x2+ax+b is. . .

Question : If one of the zeroes of a quadratic polynomial of the form of x²+ax+b is the negative of the other, then it 

a) has no linear term and the constant term is negative.
b) has no linear term and the constant term is positive.
c) can have a linear term but the constant term is negative.
d) can have a linear term but the constant term is positive.

Doubt by Zoha

Solution : 

Let α=α and β= - α

then 

sum of Zeroes

α+β=-b/a
α+(-α)=-b/a

0=-b/a
b = 0

Clearly, linear term (term having x) is zero.

Product of Zeroes

αβ=c/a
α(-α) = c/a
-α²=c/a
c=-aα²

Clearly, constant term is negative.

Hence, a) has no linear term and the constant term is negative, is the correct option.