Which among the following equations has roots that are negatives of the roots of the equation $x^3-x^2+x-4=0$?

Let $f(x)=ax^{2}+bx+c$ and $g(x)=px^{2}+qx+r$ such that $f(1)=g(1)$,$f(2)=g(2)$ and $f(3)-g(3)=2$. Then,$f(4)-g(4)$ is:

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

If one root of the equation $x^2 + px + q = 0$ is $2 + \sqrt{3}$,then the values of $p$ and $q$ are:

What are the real roots of the equation $x^2 + 5|x| + 4 = 0$?

Let $\alpha, \beta$ be the roots of the quadratic equation $x^2+\sqrt{6}x+3=0$. Then $\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}$ is equal to: