Question

Solve: 125x^3 + 343=0 Find all Complex Roots.

Answer 1

$125x^3+343=0 \\(5x)^3+7^3=0 \\(5x+7)(25x^2-35x+49)=0 \\25x^2-35x+49=0 \\a=25,b=-35,c=49 \\ \\x_{1,2}= \frac{-(-35)\pm \sqrt{(-35)^2-4\times25\times49} }{2\times25}=\frac{35\pm \sqrt{-3675} }{50}=\frac{35\pm i\sqrt{3675} }{50}$