$I. 24x^2 + 38x + 15 = 0$
$II. 12y^2 + 28y + 15 = 0$

The equation $\log_e x + \log_e(1 + x) = 0$ can be written as

The equation $x^{2}-p x+q=0, p, q \in R$ has no real root if:

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 $(3x - 2y) : (2x + 3y) = 5 : 6$,then one of the values of $\left(\frac{\sqrt[3]{x} + \sqrt[3]{y}}{\sqrt[3]{x} - \sqrt[3]{y}}\right)^{2}$ is

Two candidates attempt to solve the equation $x^2 + px + q = 0$. One starts with a wrong value of $p$ and finds the roots to be $2$ and $6$,and the other starts with a wrong value of $q$ and finds the roots to be $2$ and $-9$. The roots of the original equation are