The roots of the equation $a(x^2 + 1) - (a^2 + 1)x = 0$ are

Let $\alpha_1, \alpha_2, \ldots, \alpha_7$ be the roots of the equation $x^7+3x^5-13x^3-15x=0$ and $|\alpha_1| \geq |\alpha_2| \geq \ldots \geq |\alpha_7|$. Then $\alpha_1 \alpha_2 - \alpha_3 \alpha_4 + \alpha_5 \alpha_6$ is equal to $..................$.

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

If $\alpha$ and $\beta$ $(\alpha > \beta)$ are the multiple roots of the equation $4x^4 + 4x^3 - 23x^2 - 12x + 36 = 0$,then $2\alpha - \beta = $

If the roots of the given equation $(\cos p-1) x^2+(\cos p) x+\sin p=0$ are real,then

If $x^2-5x+6$ is a factor of $f(x)=x^4-17x^3+kx^2-247x+210$,then the other quadratic factor of $f(x)$ is