Let $\alpha$ and $\beta$ be the roots of $x^2-6 x-2=0$, with $\alpha>\beta$. If $a_n=\alpha^n-\beta^n$ for $n \geq 1$, then the value of $\frac{a_{10}-2 a_8}{2 a_9}$ is
$1$
$2$
$3$
$4$
The product of all real roots of the equation ${x^2} - |x| - \,6 = 0$ is
The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is
The product of the roots of the equation $9 x^{2}-18|x|+5=0,$ is
Consider the cubic equation $x^3+c x^2+b x+c=0$ where $a, b, c$ are real numbers. Which of the following statements is correct?
Let $\alpha$ and $\beta$ be the roots of the equation $5 x^{2}+6 x-2=0 .$ If $S_{n}=\alpha^{n}+\beta^{n}, n=1,2,3 \ldots$ then :