If $$1+x^2=\sqrt{3} x$$, then $$\sum_{n=1}^{24}\left(x^n-\frac{1}{x^n}\right)^2$$ is equal to

Let $$p$$ and $$q$$ be the roots of the equation $$x^2-2 x+A=0$$ and let $$r$$ and $$s$$ be the roots of the equation $$x^2-18 x+B=0$$. If $$p < q < r < s$$ are in AP then the values of $$A$$ and $$B$$ are

Let $$f(x)=x^3+a x^2+b x+c$$ be polynomial with integer coefficients. If the roots of $$f(x)$$ are integer and are in Arithmetic Progression, then $$a$$ cannot take the value