102 ◾ Computing
variable or an unknown, and a, b, c, d, and e are constants with a ≠ 0.
(If a = 0, the equation is a cubic equation at most.) A quintic equa-
tion is a polynomial equation of the h degree. e general form is
ax
5
+ bx
4
+ cx
3
+ dx
2
+ ex + f = 0. As we will see, some very intelligent and
also tragic young mathematicians showed that quintic equations do not
have a general algebraic solution (i.e., solutions in radicals). An algebraic
solution means a solution of an algebraic equation in terms of the coe-
cients relying on addition, subtraction, multiplication, division, and the
extraction of roots (i.e., radicals). For example, x
5
– x + 1 = 0 is a quintic
equation such that its roots cannot be expressed in terms ofradica ...