X^4 + 4x^3 + 4x^2 = - 16x

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Mathematics

14 July, 22:58

X^4 + 4x^3 + 4x^2 = - 16x

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Cheyanne · Answer 1

x⁴ + 4x³ + 4x² = - 16x

x⁴ + 4x³ + 4x² + 16x = - 16x + 16x

x⁴ + 4x³ + 4x² + 16x = 0

x (x³) + x (4x²) + x (4x) + x (16) = 0

x (x³ + 4x² + 4x + 16) = 0

x (x² (x) + x² (4) + 4 (x) + 4 (4)) = 0

x (x² (x + 4) + 4 (x + 4)) = 0

x (x² + 4) (x + 4) = 0

x = 0 U x² + 4 = 0 U x + 4 = 0

- 4 - 4 - 4 - 4

x² = - 4 x = - 4

x = + 2i

The solution set is equal to {-4, - 2i, 0, 2i}.