What are the real or imaginary solutions of the polynomial equation? 8x^3 + 125 = 0
A. No solution
B. 5/2, -5/2
C. -5/2,5+-5isqrt3/4
D. 5/2, 10i+-10isqrt3/8
The given polynomial equation is 8x^3 + 125 = 0.
To solve this equation, we can rewrite it as:
8x^3 = -125
Now, we can observe that -125 can be expressed as (-5)^3.
So, we can rewrite the equation as:
8x^3 = (-5)^3
Taking the cube root of both sides, we get:
x = -5/2
Therefore, the real solution to the polynomial equation is x = -5/2.
Hence, the correct answer is B. 5/2, -5/2.