Find all roots of the polynomial f(x) = x^4 - 5x^3 + 5x^2 + 17x - 42 + 4x^4 + 10x^3 - 18x^2 + 2x - 5.
Simplify as
5x^4 + 5x^3 - 13x^2 + 19x - 47 = 0
No rational roots are possible
WolframAlpha shows the real roots to be x ≈ -2.8195 and x ≈ 1.5644
The non-real roots are ≈ .1276 +/- 1.4542i