Solve the given two equations and select the correct answer from the given options.
$I.$ $3216 x^{2} + 3859 x + 481 = 0$
$II.$ $8132 y^{2} - 4839 y + 978 = 0$

$\frac{1}{2}(a+b+c)\{(a-b)^{2}+(b-c)^{2}+(c-a)^{2}\}=?$

If the cost price of an article is $79 \frac{2}{7} \%$ of the marked price and there is a discount of $Rs. \,68$ on the marked price,resulting in a profit of $20 \%$,find the cost price (Quantity $I$) and compare it with a given value (Quantity $II = 1200$).

Solve the given two equations and provide the correct answer from the given options.
$I.$ $x^{2}-82x+781=0$
$II.$ $y^{2}-5041=0$

If the roots of the equation $x^2 + px + q = 0$ differ by $1$,then:

If $a, b, c$ are distinct real numbers and $a^3 + b^3 + c^3 = 3abc$,then the equation $ax^2 + bx + c = 0$ has two roots,out of which one root is