The value of $k$ for which the quadratic equation $(k + 11)x^2 - (k + 3)x + 1 = 0$ has real and equal roots is:

Solve the given two equations and select the correct option.
$I.$ $\frac{12}{\sqrt{x}} - \frac{23}{\sqrt{x}} = 5\sqrt{x}$
$II.$ $\frac{\sqrt{y}}{12} - \frac{5\sqrt{y}}{12} = -\frac{1}{\sqrt{y}}$

For the quadratic equation $2x^2 - (p + 1)x + (p - 1) = 0$,if $\alpha - \beta = \alpha \beta$,then what is the value of $p$?

If polynomial $P(x) = x^2 + ax + b$ has factors $(x - a)(x - b)$,where $a, b \in R$,then the value of $P(2)$ is:

If $x^{4}+\frac{1}{x^{4}}=119$ and $x>1$,then find the positive value of $x^{3}-\frac{1}{x^{3}}$.

The set of all real values of $\lambda$ for which the quadratic equation $(\lambda^{2}+1) x^{2}-4 \lambda x+2=0$ has exactly one root in the interval $(0,1)$ is