For $$a\ne b$$, if the equation $$x^2+ax+b=0$$ and $$x^2+bx+a=0$$ have a common root, then the value of $$a+b$$ is equal to

If the product of the roots of $$9x^3+112x^2-120x+a=0$$ is 12, then the value of $$a$$ is

$$2+\sqrt{5}, 1$$ are roots of the cubic equation given by

If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2+x+1=0$$, then the equation whose roots are $$\alpha^{2021}, \beta^{2021}$$ is given by