MAT103

Franklin College

Erich Prisner

Given are the infinitely many cubic equations

.......

x^{3} -3x + 10 = 0

x^{3} -2x + 10 = 0

x^{3} -x + 10 = 0

x^{3} + 10 = 0

x^{3} +x + 10 = 0

x^{3} +2x + 10 = 0

x^{3} +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
x^{3} -10x + 10 = 0. Which of these infinitely many equations has three
real solutions?

Erich Prisner, August 2003