Solve the given two equations and select the correct answer from the given options.
$I.$ $2x + 5y = 6$
$II.$ $5x + 11y = 9$

The values of $a$ and $b$ for which the equation $x^4 - 4x^3 + ax^2 + bx + 1 = 0$ has four real roots are:

If the roots of the equation $qx^2 + px + q = 0$,where $p$ and $q$ are real,are complex,then the roots of the equation $x^2 - 4qx + p^2 = 0$ are

The number of integers satisfying the inequality $\sqrt{\log_3(x) - 1} + \frac{\frac{1}{2}\log_3(x^3)}{\log_3(\frac{1}{3})} + 2 > 0$ is

If $\alpha_1, \alpha_2$ and $\beta_1, \beta_2$ are the roots of the equations $ax^2 + bx + c = 0$ and $px^2 + qx + r = 0$ respectively,and the system of equations $\alpha_1 y + \alpha_2 z = 0$ and $\beta_1 y + \beta_2 z = 0$ has a non-zero solution,then:

If a root of the given equation $a(b - c)x^2 + b(c - a)x + c(a - b) = 0$ is $1$,then the other root will be