If $1$ is the solution of a quadratic equation $3x^{2}-kx+2=0$,then $k=\ldots$

If the roots of the following quadratic equation exist,find them by the method of completing the square: $(2x + 1) - \frac{4}{(2x + 1)} - 3 = 0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $x^{2}-(k+10)x+9(k+1)=0$.

Write whether the following statements are true or false. Justify your answers.
$(i)$ If the coefficient of $x^{2}$ and the constant term have the same sign and if the coefficient of $x$ term is zero,then the quadratic equation has no real roots.
$(ii)$ Every quadratic equation has at least two roots.

Divide $16$ into two parts such that twice the square of the larger part exceeds the square of the smaller part by $164$.

Find the discriminant of the following quadratic equation: $\sqrt{5} x^{2}-2 \sqrt{2} x-2 \sqrt{5}=0$.