For what possible values of $a$ does $6$ lie between the roots of the equation $x^2 + 2(a - 3)x + 9 = 0$?

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

If both the roots of the quadratic equation $x^2 - 2kx + k^2 + k - 5 = 0$ are less than $5$,then $k$ lies in the interval:

The quadratic expression $(2x+1)^{2} - px + q \neq 0$ for any real $x$, if

If $ax^2 + bx + c < 0$ for all $x \in R$ and the expressions $cx^2 + ax + b$ and $ax^2 + bx + c$ have their extreme values at the same point $x$,then for the expression $cx^2 + ax + b$:

If the roots of the equation $x^2+x+a=0$ exceed $a$,then