The dilemma is the sign

Algebra Level 3

Let $a, b$ and $c$ be arbitrary real numbers such that $a+b+c>0$ and $b^{2}<4ac.$ Which of the following is right about the sign of $a$ ?

a

must be always negative.

a

must be always positive.

a

can be positive, negative or zero.

a

can be positive or negative but not zero.

a

must be always zero.