Solve the given two equations and select the correct answer from the given options.
$I.$ $7x^2 + 16x - 15 = 0$
$II.$ $y^2 - 6y - 7 = 0$

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $ax^2 + bx + c = 0$. If $a, b, c$ are in $A.P.$ and $\alpha + \beta = 15$,then $\alpha\beta$ equals:

If the roots of the equation $ax^2 + x + b = 0$ are real,then the roots of the equation $x^2 - 4\sqrt{ab}x + 1 = 0$ will be

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 $II = 1200$).

If $\alpha$ and $\beta$ are the roots of the equation $lx^2 + mx + n = 0$,then the equation whose roots are $\alpha^3\beta$ and $\alpha\beta^3$ is:

Solve the given two equations and select the correct answer from the given options.
$I.$ $6x^2 + 77x + 121 = 0$
$II.$ $y^2 + 9y - 22 = 0$