Bob T. answered • 11/02/14

Effective, Patient, and Resourceful Math Tutor

Finding the zeroes of the function p = 0 means that p(x) = 0, and therefore, x^3 – 3x^2 + 4x – 12 = 0

We would have a line of the coefficients 1, -3, 4, and -12;

Next, place the 3, representing the factor (x-3):

3 0 12

1 0 4 0 for x^2 + 0 x^1 + 4, or x^2 + 4

From this latter part, we have something

*similar*to the special polynomial or quadratic product x^2 - 4. However, this product is

*not*one of the special products we know, nor do we have this factor as a part of our solution.

From this, we subtract 4 on both sides, which implies that

([-2]i)^2 = ([-2]^2)(i^2) = (4)(-1) = -4

(2i)^2 = (2^2)(i^2) = (4)(-1) = -4

Remember: Every imaginary or complex solutions come in pairs. The imaginary part is in the form x±c, where c , in our case, is ±2i, where the real part is 0: 0±2i

⇒ (implies [that]) x = {0-2i, 0+2i, 3}, or x = {-2i, 2i, 3}.