Find all real and imaginary zeros 1.) 343x^3-8=0 2.) 64x^3=0

1. 343x³ - 8 = 0

343x³ + 98x² - 98x² + 28x - 28x - 8 = 0

343x³ + 98x² + 28x - 98x² - 28x - 8 = 0

7x (49x²) + 7x (14x) + 7x (4) - 2 (49x²) - 2 (14x) - 2 (4) = 0

7x (49x² + 14x + 4) - 2 (49x² + 14x + 4) = 0

(7x - 2) (49x² + 14x + 4) = 0

7x - 2 = 0 or 49x² + 14x + 4 = 0

+ 2 + 2 x = - (14) ± √ ((14) ² - 4 (49) (4))

7x = 2 2 (49)

7 7 x = - 14 ± √ (196 - 784)

x = ²/₇ 98

x = - 14 ± √ (-588)

-98

x = - 14 ± 14i√ (3)

-98

x = - 14 + 14i√ (3) or x = - 14 - 14i√ (3)

-98 - 98

x = ¹/₇ - ¹/₇i√ (3) or x = ¹/₇ + ¹/₇√ (3)

x = ¹/₇ ± ¹/₇i√ (3)

Solution Set: {¹/₇ ± ¹/₇i√ (3), ²/₇}

2. 64x³ = 0

64 64

x³ = 0

∛ (x³) = ∛ (0)

x = 0

Solution Set: {0}