If the product of the roots of the equation $mx^2 + 6x + (2m - 1) = 0$ is $-1$,then the value of $m$ 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 $II = 1200$).

Solve the given two equations and select the correct answer from the given options.
$I.$ $8x^2 + 6x = 5$
$II.$ $12y^2 - 22y + 8 = 0$

Two candidates attempt to solve the equation $x^2 + px + q = 0$. One starts with a wrong value of $p$ and finds the roots to be $2$ and $6$,and the other starts with a wrong value of $q$ and finds the roots to be $2$ and $-9$. The roots of the original equation are

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 2x + 3 = 0$,then the equation whose roots are $\frac{1}{\alpha^2}$ and $\frac{1}{\beta^2}$ is:

Solve the given two equations and select the correct answer from the given options.
$I.$ $12x + 3y = 14$
$II.$ $4x + 2y = 16$