What are the real and complex solutions of the polynomial equation x³ - 8 = 0

Solution:

Given polynomial equation x³ - 8 = 0

x³-8 is a cubic polynomial is in the form a³ - b³ = (a - b)(a² + ab + b²)

x³ - 2³ = (x - 2)(x² + 2x + 4)

One root is 2

x² + 2x + 4 = 0

x = -b ± √(b² - 4ac) / 2a

x = -2 ± √2² - 4(4) /2

x = -2 ± √4 - 16 /2

x = -2 ± √-12 /2

x = -1 ± √3i

Therefore, x = 2, -1 ±√3i

What are the real and complex solutions of the polynomial equation x³ - 8 = 0

Summary:

The real and complex solutions of the polynomial equation x³ - 8 = 0 are 2 and -1 ±√3i respectively.