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

For what interval of $m$ do all roots of the quadratic equation $x^2 - 2mx + m^2 - 1 = 0$ lie between $-2$ and $4$?

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 the graph of $y = ax^2 + bx + c$ $(a, b, c \in R)$ is as shown in the figure,where $D = b^2 - 4ac$,which of the following is incorrect?

The number of integral values of $m$ for which the quadratic expression $(1 + 2m)x^2 - 2(1 + 3m)x + 4(1 + m)$ is always positive for all $x \in R$ is:

If the roots of the quadratic equation $x^2 - 2kx + k^2 + k - 5 = 0$ are less than $5$,then in which interval does $k$ lie?