If both the roots of a quadratic equation $kx^{2} + 4x + 1 = 0$ are equal,then $k = \ldots$

If the roots of the equation $6x^2 - 13x + m = 0$ are reciprocal of each other,then $m = $ ...........

If one of the roots of the equation $px^{2} + qx + r = 0$ where $p \neq 0$ and $p, q, r \in R$ is $x = -2$,then prove that $4p - 2q + r = 0$.

Examine whether the following equation is quadratic or not: $x^{3}-4x^{2}-x+1=(x-2)^{3}$

Solve the following equation using the method of factorization: $\frac{x^{2}-1}{x^{2}+1}=\frac{7}{9}$

At $t$ minutes past $2\, pm$, the time needed by the minute hand of a clock to show $3\, pm$ was found to be $3\, minutes$ less than $\frac{t^{2}}{4}$ $minutes$. Find $t$.