Question

What are the real or imaginary solutions of the polynomial equation?

27x3 + 125 = 0
steps too please.

Answer 1

factor as the sum of two cubes
\[a^3+b^3=(a+b)(a^2-ab+b^2)\] use \(a=3x,b=5\)

Answer 2

then set each factor equal to zero and solve
the first answer will be obvious, the second requires the quadratic formula for the two complex zeros

Answer 3

That's a good formula @satellite73 thanks. I was considering just solving for x and using synthetic division to get rid of the discovered root.