Cardano method for cubic equations

The roots of quadratic and cubic equations are well known as algebraic expressions of the equation s coefficients, and hence this section is comletely disconnected from the rest of the chapter. Nevertheless, these simple problems are so frequently encountered that we cannot ignore their special solutions. 

You certainly know how to solve a quadratic equation, but we provide a routine for solving the cubic equation 

Since 0 (otherwise we have a quadratic equation), introducing the variable x=y-B/(3A), (2.3) can be reduced to the form 

We first evaluate the discriminant d = (p/3)3 + (q/2)2. If d 0, then the cubic equation has three (but not necessarily different) real roots. If, on the other hand, d 0, then the equation has one real root and a conjugate pair of complex roots. Since you find the expressions for the roots in mathematical tables we proceed to the module. 

2040 P0=B/A/3s Pl=C/A/3-P0IP0 P2=P0 P0JP0t(O-CtP0 /2/fi 2842 IF PIO0 THEN 204B 

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