Let $p, q, r \in \mathbb{R}$ and $r > p > 0.$ If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha$ and $\beta,$ then $|\alpha| + |\beta|$ is:

If $10$ men and $15$ women complete a piece of work in $8$ days,while $12$ men and $8$ women can complete the same piece of work in $10$ days. $A$ boy,who is $50 \%$ less efficient than a man,can do the same work in $50$ days.
$Quantity \, I$: Time taken by $2$ men,$4$ women,and $18$ boys to complete the work.
$Quantity \, II$: Time taken by $9$ men,$3$ women,and $6$ boys to complete the same work.

In the following,determine the set of values of $P$ for which the given quadratic equation $Px^2 + 4x + 1 = 0$ has real roots.

Solve the given two equations and select the correct option.
$I.$ $x^{2}-4=0$
$II.$ $y^{2}+6y+9=0$

${x \in R : |x - 2| = x^2} = $

If the roots of the equation $ax^2 + bx + c = 0$ are reciprocal to each other,then: