If the roots of the equation $x^2 + px + q = 0$ differ by $1$,then:

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

$Quantity \, 1$: Time taken by Manoj and Shubham to complete the work together. When Manoj works alone,he takes $4.8 \, \text{hrs}$ more than the time taken by Manoj and Shubham to complete the work together. When Shubham works alone,he takes $10.8 \, \text{hrs}$ more than the time taken by both of them to complete the work together.
$Quantity \, 2$: $7.4 \, \text{hrs}$.

If the roots of the equation $ax^2 + bx + c = 0$ are reciprocal to each other,then:

The number which exceeds its positive square root by $12$ is

The value of $k$ for which the equation $(K - 2)x^2 + 8x + K + 4 = 0$ has both roots real,distinct and negative is