Solving Polynomial Equations from Complex Numbers

We show that a polynomial equation of degree less than 5 and with real parameters can be solved by regarding the variable in which the polynomial depends as a complex variable. For do it so, we only have to separate the real and imaginary parts of the resultant polynomial and solve them separately.

💡 Research Summary

The paper claims that any polynomial of degree less than five with real coefficients can be solved by treating the indeterminate (x) as a complex variable (z=a+ib), separating the resulting expression into its real and imaginary parts, and then solving the two resulting real equations independently. The authors begin by recalling that closed‑form solutions by radicals exist for degrees up to four, while the general quintic is unsolvable in radicals, and they suggest that a complex‑variable approach might bypass this limitation.

In the main section they substitute (z=a+ib) into a generic polynomial
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