What are the roots of the polynomial equation x^4+x^3=4x^2+4x? - 2, - 1, 0, 2 - 2, 0, 1, 2 - 1, 0 0, 1

Question

Mathematics

Nick Hawkins

30 April, 07:16

What are the roots of the polynomial equation x^4+x^3=4x^2+4x? - 2, - 1, 0, 2 - 2, 0, 1, 2 - 1, 0 0, 1

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Cookie · Answer 1

x⁴ + x³ = 4x² + 4x

x⁴ + x³ - 4x² - 4x = 0

x (x³) + x (x²) - x (4x) - x (4) = 0

x (x³ + x² - 4x - 4) = 0

x (x² (x) + x² (1) - 4 (x) - 4 (1)) = 0

x (x² (x + 1) - 4 (x + 1)) = 0

x (x² - 4) (x + 1) = 0

x (x² + 2x - 2x - 4) (x + 1) = 0

x (x (x) + x (2) - 2 (x) + 2 (2)) (x + 1) = 0

x (x (x + 2) - 2 (x + 2)) (x + 1) = 0

x (x - 2) (x + 2) (x + 1) = 0

x = 0 U x - 2 = 0 U x + 2 = 0 U x + 1 = 0

+ 2 + 2 - 2 - 2 - 1 - 1

x = 2 x = - 2 x = - 1

Solution Set: {-2, - 1, 0, 2}