If $a_1,a_2,a_3$ are roots $x^3+7x^2-8x+3,$ find the polynomial with roots $a_1^2,a_2^2,a_3^2$ If $a_1,a_2,a_3$ are the roots of the cubic $x^3+7x^2-8x +3,$ find the cubic polynomial whose roots are:
$a_1^2,a_2^2,a_3^2$ and the polynomial whose roots are $\frac{1}{a_1}, \frac{1}{a_2}, \frac{1}{a_3}.$ Not really sure where to go. Hints appreciated. 

For the second,
if
$f(x) 
= x^3+ux^2+vx+w
=0
$
then,
if
$g(x)
=x^3f(1/x)
= x^3(1/x^3+u/x^2+v/x+w)
= 1+ux+vx^2+wx^3
$
$g(x)$
 has the same roots as
$f(1/x)$
as long as none of the roots
are zero.
Therefore,
just reverse the order of the coefficients:
$3x^3-8x^2+7x+1$.
