Question

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

27x3 + 125 = 0
steps too please.

Answer 1

the left hand side is a sum of two cubes: (3x)^3+(5)^3

Answer 2

let's factor the sum of two cubes into \[(3x+5)(9x^2-15x+25)\]

Answer 3

and equate each factor to zero. the first factor yields a real solution, the second factor yields two complex roots by using the quadratic formula