33.4 Roots of Quartic Polynomials

Solutions to the quartic polynomial equation

$$x^4+a_3x^3+a_2x^2+a_1x+a_0 = 0,$$ (33.3)

where $a_3$,$a_2$,$a_1$ and $a_0$ are all real, are found again by Newton-Raphson and bisection iterations techniques, even for quartics possessing only complex roots. Please consult Flocke 2015 for the theoretical and computational details.