The first meaningful interest in polynomial equations of third degree in
Europe came with Leonardo Pisano (otherwise known as Fibonacci, 1178-?), who
was at one point asked by Frederick II to solve the cubic equation
. Fibonacci showed first that no rational solution could
exist, by dividing through by 10 and substituting supposing
the fraction reduced so that hcf(a,b)=1. This gathers
which is impossible as the highest common factor of a and b was supposed to be 1. Hence . Using similar procedures Fibonacci showed that the solution could not even be in any of the forms , , , . He then used an approximate method that allowed him to recover one of the roots to an approximation of about ten digits. It is not known what was the method involved, but it may be Horner's method, which was already known by the Chinese.