Question

How do find all zeros of the function?

`g(x)=x^(4)-3x^(3)-x^(2)-12x-20`

`x=2i`

Answer 1

`x=+-2i,x=(3+-sqrt(29))/2`

Explanation:

We have been given that `x=2i` is a zero. Since complex solutions to polynomials with real coefficients always come in conjugate pairs (the imaginary parts need to cancel), we know that `x=-2i` is also a solution.

This means that `(x-2i)(x+2i)=x^2+4` is a factor of the polynomial, and we can find out the remainder using polynomial long division:
`(x^2+4)(x^2-3x-5)`

We can solve for when the quadratic factor equals zero using the quadratic formula:
`x=(3+-sqrt(29))/2`