If one root of a

If one root is imaginary that means the equation has no real root.

(since the equation has real co efficients complex roots must occur in conjugate pair, and a quadratic equation has only two roots,this is known as fundamental theorem of algebra an can be generalized for any degree)

so the equation is either always positive or always negative.

we have supplied 8a + 2b >c

looking closely you will find that it means a(4)^2 + b(4) - 2c >0

so we have established that the function f(x) = a(x)^2 + b(x) - 2c >0

so 'a' must be positive..(if u can't find why try giving x a very large negative value )

and also f(0) >0 or -2c>0 or c<0

thanks