Which value is NOT a solution of x^3 + 64 = 0? (MULTIPLE CHOICE)

Question

Which value is NOT a solution of x³ + 64 = 0?

 

a. 2+2i√3

b. 2-2i√3
c. 4
d. –4

Answer 1

x³ + 64 = 0 can be written as x³ + 4³ = 0, which is the sum of two cubes.            [  a³ + b³ = (a + b)(a² - ab + b²)  ]

 

This factors into (x + 4)(x² - 4x + 16) = 0

So x = -4 or (solving x² - 4x + 16 = 0 using the quadratic formula, or by completing the square) x = 2±2i√3

 

x cannot = 4, so the answer is c