Here, I will post puzzles with details as following.
Each Sunday, I will post a puzzle.
$\textbf{Question(NBHM June 2005)}$ Find the value of $\textbf{a}$ such that $2+\sqrt{3}$ is a root of the polynomial,
$$
x^3-5x^2+ax-1
$$
Here I will put note to solve the problem and keep brushing the knowledge.