If $a$ and $b$ are roots of $x^2 - px + q = 0$,then $\frac{1}{a} + \frac{1}{b} = $

Let $\alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of $x^2 - 4x + q = 0$. If $\alpha, \beta, \gamma, \delta$ are in $G.P.$,then the integral values of $p, q$ are respectively:

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

The number of roots of the quadratic equation $8\sec^2 \theta - 6\sec \theta + 1 = 0$ is

The condition for the roots of the equation $(c^2 - ab)x^2 - 2(a^2 - bc)x + (b^2 - ac) = 0$ to be equal is

Solve the given two equations and choose the correct option.
$I. 20 x^{2}-67 x+56=0$
$II. 56 y^{2}-67 y+20=0$