What are the real or imaginary solutions of the polynomial equation? 8x^3 + 125 = 0

Answer 1

To find the solutions of the equation 8x^3 + 125 = 0, we need to set the expression equal to zero:

8x^3 + 125 = 0

We can rewrite this equation as:

8x^3 = -125

To isolate x, we can divide both sides of the equation by 8:

x^3 = -125/8

Now, we can take the cube root of both sides to solve for x:

x = ∛(-125/8)

Using a calculator, we find that ∛(-125/8) ≈ -2.5

Thus, the real solution to the equation 8x^3 + 125 = 0 is x = -2.5.

There are no imaginary solutions to this equation since all the terms are real.