If the polynomial

a

_{n}x

^{n}+a

_{n-1}x

^{n-1}+a

_{n-2}x

^{n-2}+.....+a

_{0}

has roots r

_{0}, r

_{1}, r

_{2}, ....., r

_{n},

then the polynomial with roots (r

_{0})

^{2}, (r

_{1})

^{2}, (r

_{2})

^{2}, ....., (r

_{n})

^{2}, is such that every term can be worked out by this "formula"

(-1)

^{n-k}[(a

_{k})

^{2}-2[(a

_{k-1})(a

_{k+1})-(a

_{k-2})(a

_{k+2})+(a

_{k-3})(a

_{k+3})-.....]]x

^{k}

where k is the value of the current term being operated on. In other words, a polynomial ax

^{6}+bx

^{5}+cx

^{4}+dx

^{3}+ex

^{2}+fx+g has roots r

_{0}, r

_{1}, r

_{2}, ....., r

_{6}. The polynomial with roots (r

_{0})

^{2}, (r

_{1})

^{2}, (r

_{2})

^{2}, ....., (r

_{6})

^{2}is

a

^{2}x

^{6}-(b

^{2}-2ac)x

^{5}+(c

^{2}-2(bd-ae))x

^{4+}(d

^{2}-2(ce-bf+ag))x

^{3}+(e

^{2}-2(df-cg))x

^{2}+(f

^{2}-2eg)x+g

^{2}

Cool, huh? I wasted my life figuring that out on paper, I even had to learn the character for six in the greek alph. stigma. weird, it doesn't exist in the alphabet anymore, bet that confuses some people.

EDIT: fixerising. these sups and subs are retarded, you can barely see anything when you're editing.