Solve the given two equations and select the correct answer from the given options.
$I.$ $13x - 21 = 200 - 4x$
$II.$ $y = \sqrt[3]{2197}$

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

If $3$ is a root of the equation ${x^2} + kx - 24 = 0,$ then $3$ is also a root of which of the following equations?

The expression $y = ax^2 + bx + c$ has always the same sign as $c$ if

Two students,while solving a quadratic equation in $x$,one copied the constant term incorrectly and got the roots $3$ and $2$. The other copied the constant term and coefficient of $x^2$ correctly as $-6$ and $1$ respectively. The correct roots are:

Let $p(x)$ be a quadratic polynomial such that $p(0) = 1$. If $p(x)$ leaves a remainder of $4$ when divided by $x - 1$ and a remainder of $6$ when divided by $x + 1$,then: