Question

Solve the following equation by identifying all of its roots including all real and complex numbers. In your final answer, include the necessary steps and calculations. Hint: Use your knowledge of factoring polynomials.

(x^2+1)(x^3+2x)(x^2-64)=0

Answer 1

x² + 1 = 0
x² = - 1
x 1 = i, x 2 = - i
x³ + 2 x = 0
x ( x² + 2 ) = 0
x 3 = 0
x² + 2 = 0
x² = - 2
x 4 = √2 i, x 5 = - √2 i
x² - 64 = 0
x² = 64
x 6 = - 8, x 7 = 8
Answer:
All roots are: { -√2 i, -i, i, √2 i, - 8, 0, 8 }