Writing Project 16:

Solving cubic equations

Given are the infinitely many cubic equations
.......
x³ -3x + 10 = 0
x³ -2x + 10 = 0
x³ -x + 10 = 0
x³ + 10 = 0
x³ +x + 10 = 0
x³ +2x + 10 = 0
x³ +3x + 10 = 0
.......

For which of these infinitely many equations does our approach, using the rational zeros theorem, long division, and the quadratic formula, work?

Look the so-called "Cardano's formula" up in the internet and use it to solve the cubic equation x³ -10x + 10 = 0. Which of these infinitely many equations has three real solutions?

Erich Prisner, August 2003