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