If $\alpha ,\beta$ are the zeroes of the quadratic polynomial
$f\left(x\right)=x^2-px+q$, then $\frac{1}{\alpha }+\frac{1}{\beta }=$

Q. If $\alpha$ and $\beta$ are the zero of the quadratic polynomial $f\left(x\right)=x^2-px+q$, that $\frac{{\alpha }^2}{{\beta }^2}+\frac{{\beta }^2}{{\alpha }^2}=\frac{p^4}{q^2}-\frac{{4p}^2}{q^2}+2$

Q. If $\alpha ,\beta$ are zeroes of polynomial $f\left(x\right)=x^2+px+q$ then polynomial having $\frac{1}{\alpha }$ and $\frac{1}{\beta }$ as its zeroes is :

Q.

If α&β are zeros of the polynomial f(x)=x²+px+q,then find a polynomial having 1/α & 1/β as its zeros.

Q. If $\alpha$ and $\beta$ are the roots of the equation $x^2-px+q=0,$ then find the equation whose roots are $\frac{q}{p-\alpha }$ and $\frac{q}{p-\beta }$

Q. Let $p$ and $q$ be real numbers such that $p\ne 0,p^3\ne q$ and $p^3\ne -q$. If $\alpha$ and $\beta$ are non zero complex numbers satisfying $\alpha +\beta =-p$ and ${\alpha }^3+{\beta }^3=q$, then a quadratic equation having $\frac{\alpha }{\beta }$ and $\frac{\beta }{\alpha }$ as its roots is