If the sum of the roots of a quadratic equation is $1$ and the product of the roots is $-20$, find the quadratic equation.

If the equation $(m - n)x^2 + (n - l)x + l - m = 0$ has equal roots,then $l, m$ and $n$ satisfy:

An equation equivalent to the quadratic equation $x^{2}-6x+5=0$ is:

$A$ man who swims $48 \, m/min$ in still water,swims $200 \, m$ against the current and $200 \, m$ with the current. The difference between the time taken by him against the stream and with the stream is $10 \, minutes.$
$Quantity \, 1$: Speed of current.
$Quantity \, 2$: Speed of a man who completes $3$ rounds of a circular path of radius $49 \, m$ in $14 \, minutes.$

All the pairs $(x, y)$ that satisfy the inequality $2^{\sqrt{\sin^2 x - 2\sin x + 5}} \cdot \frac{1}{4^{\sin^2 y}} \leq 1$ also satisfy the equation:

The sum of all the real values of $x$ satisfying the equation $2^{(x - 1)(x^2 + 5x - 50)} = 1$ is