Question

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

Answer 1

Answer: The answer Is A

Answer 2

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}