If $y = f(x) = ax^2 + 2bx + c = 0$ has imaginary roots and $4a + 4b + c < 0$,then :-

Let $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$,where $x \in R$. If $b$ and $c$ are nonzero real numbers such that $\min f(x) > \max g(x)$,then $\left|\frac{c}{b}\right|$ lies in the interval:

If non-zero real numbers $p$ and $q$ exist such that $\min f(x) > \max g(x)$,where $f(x) = x^2 + 2px + 2q^2$ and $g(x) = -x^2 - 2qx + p^2$ for $x \in \mathbb{R}$,find the set of values containing $|\frac{2p}{q}|$.

If $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$ such that $\min f(x) > \max g(x)$,then the relation between $b$ and $c$ is

If both the roots of the equation $x^2 - 6ax + 2 - 2a + 9a^2 = 0$ exceed $3$,then

All the values of $k$ such that the quadratic expression $2kx^2 - (4k+1)x + 2$ is negative for exactly three integral values of $x$,lie in the interval