Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations. Hint: Use your knowledge of factoring polynomials and identities for imaginary numbers.

x^3-27i

Question

Anabella Graves

Mathematics

20 August, 19:34

Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations. Hint: Use your knowledge of factoring polynomials and identities for imaginary numbers.

x^3-27i

+1

Answers (1)

Know the Answer?

Jimmy Schwartz · Answer 1

I^3=-i

therefor - 27i = (3i) ^3

so we can get a sum of 2 perfect cubes

a^3+b^3 = (a+b) (a^2-ab+b^2)

so

remember that i²=-1

x^3 + (3i) ^3 = (x+3i) (x²-3xi-1)

Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations. Hint: Use your knowledge of factoring polynomials and identities for imaginary numbers.x^3-27i

Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations. Hint: Use your knowledge of factoring polynomials and identities for imaginary numbers.

x^3-27i