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

State whether the quadratic equation $3 x^{2}-4 x+1=0$ has two distinct real roots. Justify your answer.

Is $0.2$ a root of the equation $x^{2}-0.4=0$? Justify.

The hypotenuse of a garden in the shape of a right triangle is $1$ metre more than twice the shortest side. If the longer side containing the right angle is $7$ metres more than the shorter side,find the sides of the garden.

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $\frac{1}{x} - \frac{1}{x-2} = 3, x \neq 0, 2$.

If one of the roots of $x^{2}-2x-c=0$ is $5$,the other root is ...........