If $\alpha, \beta$ are the roots of the equation $x^2 - 6x - 2 = 0$,$\alpha > \beta$ and $a_n = \alpha^n - \beta^n$,$n > 1$,then the value of $\frac{a_{10} - 2a_8}{2a_9}$ is equal to

For the equation $\frac{1}{x + a} - \frac{1}{x + b} = \frac{1}{x + c}$,if the product of the roots is zero,what is the sum of the roots?

If one of the roots of the equation $x^2+px+q=0$ is equal to the square of the other,then:

Sachin and Rahul solve a quadratic equation. Sachin makes a mistake in writing the constant term and obtains roots $(4, 3)$. Rahul makes a mistake in writing the coefficient of $x$ and obtains roots $(3, 2)$. What are the correct roots of the equation?

If the roots of the equation $ax^2 + bx + c = 0$ are $\sin \alpha$ and $\cos \alpha$,then:

If $\alpha, \beta, \gamma$ are the roots of $x^3+2x+5=0$,then $\sum \frac{\beta+\gamma}{\alpha^2} = $