# How do you determine the remaining zeroes for #g(x)=2x^5-3x^4-5x^3-15x^2-207x+108# if 3i is a zero?

##### 1 Answer

Use conjugate zeros, factor theorem, division of polynomials, rational zeros theorem, division (again), then solve the resulting quadratic by you favorite method for quadratics.

#### Explanation:

**First Two Zeros**

Given that

The Factor Theorem tells us that

Divide

**Third Zero**

To find another zero, we need a zero of

Neither of the easiest choices,

Possible rational zeros are:

Test until you find a zero. (Synthetic division is recommended for this testing.)

Depending on the order in which you test, you'll find a rational zero.

I found

**Last Two Zeros**

Solve

So the final two zeros of

**List of Zeros**

Zeros: