The roots of the equation $x^2 - \sqrt{13}x + 1 = 0$ are:

Solve the given two equations and select the correct answer from the given options.
$I. 2x^2 + 3x + 1 = 0$
$II. 12y^2 + 7y + 1 = 0$

The equation $x^{(3/4)(\log_2 x)^2 + (\log_2 x) - 5/4} = \sqrt{2}$ has

Consider the equation $px^2 + qx + r = 0$,where $p, q, r$ are real. The roots are equal in magnitude but opposite in sign when

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.

The set of all real values of $\lambda$ for which the quadratic equation $(\lambda^{2}+1) x^{2}-4 \lambda x+2=0$ has exactly one root in the interval $(0,1)$ is