Question

If alpha and beta are two zeros of the quadratic polynomial x^2-1 find a quadratic polynomial whose zeros 2alpha / beta and 2 beta/alpha

Answer 1

It is easy to find the zeroes of given quadratic : 
$x^2-1=0\\x^2=1\\x=-1,~1$

Letting $\alpha=-1$ and $\beta=1$
$2\frac{\alpha}{\beta}=2\frac{-1}{1}=-2$
$2\frac{\beta}{\alpha}=2\frac{1}{-1}=-2$

Therefore a quadratic with these zeroes is $(x-(-2))(x-(-2))=\boxed{x^2+4x+4}$