If $3$ is a root of the quadratic equation $x^{2}-kx+6=0$,then $k = \ldots$

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.

If both the roots of a quadratic equation $ax^2 + bx + c = 0$ $(a \neq 0)$ are equal,then ..... .

The denominator of a non-zero ratio is one less than twice the numerator. If the sum of the ratio and its reciprocal is $2 \frac{4}{15},$ find the ratio.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + x - 3 = 0$

Examine whether the following equation is quadratic or not: $x^{2}+2 \sqrt{x}+3=0$