If $3$ is a root of $x^2 + kx - 24 = 0$,it is also a root of

If $P(x)=ax^{2}+bx+c$ and $Q(x)=-ax^{2}+dx+c$, where $ac \neq 0$ ($a, b, c, d$ are all real), then $P(x) \cdot Q(x)=0$ has

If $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \text{to } \infty}}}$,then

If $f(x)=2 x^4-13 x^2+a x+b$ is divisible by $x^2-3 x+2$,then $(a, b)$ is equal to

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

If $1-i$ is a root of the equation $x^2+ax+b=0$,then $b$ is equal to