The Polynomial f(x)= 3x^3 - 4x^2 + 27x -36 has 3i as a root, give all of the roots

Question

The Polynomial f(x)= 3x^3 - 4x^2 + 27x -36 has 3i as a root, give all of the roots of f in a comma-separated list, including the given one.

Roots :...……….

Thanks a lot

Answer 1

Since 3i was given, that tells you that -3i must also be a root.

The factors using these 2 are (x-3i)(x+3i) and if I multiply these together, you get a factor of x^2+9

Next, you have to do long division:

(3x^3 - 4x^2 + 27x -36)/(x^2+9) = 3x-4

If you set 3x-4=0 and solve, you get the last root.x=4/3

The 3 roots are: 4/3, 3i, -3i