Find the value of $a^{2}+b^{2}+c^{2}-2ab-2bc-2ca$ when $a=17, b=15$ and $c=13$.

$I. 6x^2 + 41x + 63 = 0$
$II. 4y^2 + 8y + 3 = 0$

The surface area of a pipe,open at both ends,is equal to $628 \, m^2$. The difference between its length and its radius is $15 \, m$. If the pipe were closed at one end,what amount of water could it hold (in $, m^3$)?

If one root of the quadratic equation $ix^2 - 2(i + 1)x + (2 - i) = 0$ is $2 - i$,then the other root is

The value of $a (a \ge 3)$ for which the sum of the cubes of the roots of $x^2 - (a - 2)x + (a - 3) = 0$ assumes the least value is

Form a quadratic equation whose one root is $3-\sqrt{5}$ and the sum of roots is $6$.