Question

solve and find the complex roots of 125x^3 + 343 = 0

Answer 1

sum of two cubes
\[a^3+b^3=(a+b)(a^2-ab+b^2)\] in this case you have
\[(5x)^3+7^3\]

Answer 2

factor as
\[(5x+7)(25x^2-35x+49)\]

Answer 3

one root is
\[-\frac{7}{5}\] other two complex roots via the quadratic formula

Answer 4

so I use the quad formula for the 25x^2 - 35x + 49 right?

Answer 5

Yes

Answer 6

okay thanks

Answer 7

\[x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}\]