The least integer $k$ which makes the roots of the equation ${x^2} + 5x + k = 0$ imaginary is

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-16x+63=0$
$II.$ $y^{2}-2y-35=0$

$I. \quad p^{2}-18 p+77=0$
$II. \quad 3 q^{2}-25 q+28=0$
$Quantity \, 1$: Value of $p$
$Quantity \, 2$: Value of $q$

If the equations $2ax^2 - 3bx + 4c = 0$ and $3x^2 - 4x + 5 = 0$ have a common root,then $\left( \frac{a + b}{c} \right)$ is equal to (where $a, b, c \in R$).

If the roots of $x^2 - bx + c = 0$ are two consecutive integers,then $b^2 - 4c$ is

The product of all real roots of the equation ${x^2} - |x| - 6 = 0$ is