If $$f(x)=2x^3+mx^2-13x+n$$ and 2, 3 are the roots of the equation $$f(x)=0$$, then the values of m and n are

If $$\alpha$$ and $$\beta$$ are the roots of $$11 x^2+12 x-13=0$$, then $$\frac{1}{\alpha^2}+\frac{1}{\beta^2}$$ is equal to (approximately close to)

The value of $$a$$ for which the equations $$x^3+a x+1=0$$ and $$x^4+a x^2+1=0$$ have a common root is

If $$a$$ is a positive integer such that roots of the equation $$7 x^2-13 x+a=0$$ are rational numbers, then the smallest possible value of $$a$$ is