The interval of $k$ for which the equation $x^2+kx-4=0$ has its smaller root in the interval $(-1, 2)$ is:

The values of $a$ for which one root of the equation $x^2 - (a + 1)x + a^2 + a - 8 = 0$ exceeds $2$ and the other is lesser than $2$,are given by

If $b > a$,then the equation $(x - a)(x - b) = 1$ has

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 $cx^2 + ax + b$:

The values of $a$ for which the equation $2x^2 - 2(2a + 1)x + a(a + 1) = 0$ has one root less than $a$ and the other root greater than $a$ are given by:

If $b > a$,then in which interval do the roots of the equation $(x - a)(x - b) - 1 = 0$ lie?