If $c > 0$ and the equation $3ax^2 + 4bx + c = 0$ has no real root,then :-

For what set of values of $K$ do both roots of the equation $4x^2 - 20Kx + (25K^2 + 15K - 66) = 0$ lie below $2$?

If the quadratic equation $ax^2+bx+c=0$ $(a>0)$ has two roots $\alpha$ and $\beta$ such that $\alpha < -2$ and $\beta > 2$, then which of the following is true?

If $\alpha, \beta$ are the roots of $x^2+bx+c=0$,$\gamma, \delta$ are the roots of $x^2+b_1x+c_1=0$ and $\gamma < \alpha < \delta < \beta$,then $(c-c_1)^2  < $

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:

Consider the quadratic equation $(c - 5)x^2 - 2cx + (c - 4) = 0$,where $c \ne 5$. Let $S$ be the set of all integral values of $c$ for which one root of the equation lies in the interval $(0, 2)$ and the other root lies in the interval $(2, 3)$. Then the number of elements in $S$ is