polynomial roots formulae

for quadratic equations ax²+bx+c=0, with roots p and q: (2)

• p + q = -b/a

• pq = c/a

for cubic equations ax³+bx²+cx+d=0, with roots p and q and r: (3)

• p + q + r = -b/a

• pq + rp + rq = c/a

• pqr = -d/a

for quartic equations ax⁴+bx³+cx²+dx+e=0, with roots p and q and r and s: (4)

• p + q + r + s = -b/a

• pq + pr + ps + qr + qs + rs = c/a

• pqr + pqs + qrs + qrs = -d/a

• pqrs = e/a

for complex roots in a quadratic equation, how to expand brackets:

x² -2(Re(z))x + mod z²