h(x)=4x^4+15x^3+12x^2+60x-16/-2i

Question

Use the given zero to find the remaining zeros. 

I messed up this problem the first time after working an hour!!!!!

I need a quick answer and explanation.

Answer 1

Since the polynomial has degree 4, there are, at most, 4 distinct roots. Since -2i is a root, so is 2i.

 

Therefore, x-2i and x+2i are both factors, so (x-2i)(x+2i) = x²+4 is also a factor.  

 

Divide the given polynomial by x²+4 to get the other factor 4x²+15x-4.

Factor this quadratic to find the remaining roots.  

Answer 2

if -2i is a zero than so is 2i

You can divide the quartic equation by x+2i to get a cubic equation.  Since -2i is a zero, then x+2i should have no remainder.  Then you can use your other zero, 2i, and know you can divide by x-2i and get a quadratic.  Once you have a quadratic you can solve it.  Maybe it will factor easily, but if not, you can always use the quadratic formula. 

 

So the first step is knowing that imaginary roots come in pairs.  If you have one imaginary zero, you should know what the other is.  If x+2i is a factor, than so is x-2i (its complex conjugate).  Sorry but no easy way to get a solution to this one.