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

If the maximum value of $2x - 7 - ax^2$ cannot exceed $20$,then the minimum value of $a$ is

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

If $a$ and $b$ are the maximum and minimum values of the quadratic expressions $1-2x-5x^2$ and $x^2-2x+5$ respectively,then the set of all values of $x$ for which the expression $5ax^2+bx+7$ is positive,is

The maximum and minimum values of $\frac{x^2 + x + 1}{x^2 - x + 1}$ are respectively ...........

Let $f(x) = (1 + b^2)x^2 + 2bx + 1$ and $m(b)$ be the minimum value of $f(x)$. If $b$ can take any real value,what is the range of $m(b)$?