Question

Apply Cardano's method for finding the roots of 2x^3+3x^2-8x-12=0.

Answer 1

ax^3+bx^2+cx+d=0

Q=(a^2-3b)/9=1.58,

R=(2a^3-9ab+27c)/54=-1.88,

S=Q^3-R^2=0.45

w=arccos(R/Q^3)/3

x1=-2*sqrt(Q)*cos(w)-a/3=-2

x2=-2*sqrt(Q)*cos(w+2pi/3)-a/3=2

x3=-2*sqrt(Q)*cos(w-2pi/3)-a/3=-1.5