If $-3$ is a solution of $2x^{2} + 5x + k = 0$,then $k = \ldots$

State whether the following statements are true or false. Justify your answers.
$(i)$ Every quadratic equation has at most two roots.
$(ii)$ If the coefficient of $x^{2}$ and the constant term of a quadratic equation have opposite signs,then the quadratic equation has real roots.

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

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $6x^{2}-5x-1=0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $3x^{2} - 18x + k = 0$.

Solve the following equation using the method of factorization and write its solution set: $4x^{2} + 4x = 15$.