The equation $\sqrt{3x^2 + x + 5} = x - 3$,where $x$ is real,has

Let $f(x) = x^3 + a x^2 + b x + c$ be a polynomial with integer coefficients. If the roots of $f(x)$ are integers and are in Arithmetic Progression,then '$a$' cannot take the value:

For what value of $a$ does the equation $(a^2 - a - 2)x^2 + (a^2 - 4)x + a^2 - 3a + 2 = 0$ have more than two solutions?

If the roots of the equation $x^2 + a^2 = 8x + 6a$ are real,then

If $(1 - p)$ is a root of the quadratic equation $x^2 + px + (1 - p) = 0$,then its roots are:

If $b_{1} b_{2} = 2(c_{1} + c_{2})$ and $b_{1}, b_{2}, c_{1}, c_{2}$ are all real numbers,then at least one of the equations $x^{2} + b_{1} x + c_{1} = 0$ and $x^{2} + b_{2} x + c_{2} = 0$ has