If the quotient and remainder obtained when the expression $3 x^5-6 x^4+2 x^3+4 x^2-5 x+8$ is divided by the expression $x^2-2 x+3$ are $a x^3+b x^2+c x+d$ and $p x+q$ respectively, then $a b+c d=$

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12 x^4-56 x^3+89 x^2-56 x+12=0$ such that $\alpha \beta=\gamma \delta=1$ and $\frac{\alpha+\beta}{\gamma+\delta}>1$, then $\frac{\alpha+\beta}{\gamma+\delta}=$

If the equations $x^2+p x+2=0$ and $x^2+x+2 p=0$ have a common root, then the sum of the roots of the equation $x^2+2 p x+8=0$ is

If both roots of the equation $x^2-5 a x+6 a=0$ exceed 1 , then the range of ' $a$ ' is