It sounds like they're using two different meanings of "solve". "Interpolation" is a numerical method; it would be something similar to what your calculator or other software uses to find a decimal approximation of the zeroes. But it can be proven that there are polynomials which cannot be solved algebraically
It would be like if there were no such thing as square roots. Would there then be a Quadratic Formula? So could you solve all quadratics algebraically
, or would some have to be approximated from the graph?