Find the roots of the following quadratic equation by the method of completing the square: $m^{2}-18m+81=0$

Examine whether the following equation is quadratic or not: $x+\frac{1}{x}=x^{2} (x \neq 0)$

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $2x^{2} - 6x + 3 = 0$; $x = \frac{1}{2}$.

Obtain the roots of the following quadratic equation by using the quadratic formula: $2x^{2} + 5\sqrt{3}x + 6 = 0$.

State whether the following statements are true or false. Justify your answers.
$(i)$ Every quadratic equation has exactly one root.
$(ii)$ Every quadratic equation has at least one real root.

$A$ two-digit number is such that the product of its digits is $6$. When $9$ is subtracted from the number,the resulting number is the number obtained by interchanging the digits. Find the original number.