complex zeros?

Question

My teacher hasn't taught complex zeros yet and I can't find it anywhere in the book. It says find the complex zeros of the function f(x)=x³-4x²+25x-100. If I know how to find the zeros I can do the problem but I just need a little help!

Answer 1

Hi Kari,

     I always try a few small numbers to see if one of them is a root. In this case x=4 is a root i.e. 64-64+100-100=0 so you can divide the cubic polynomial by x-4 when you do that you get x²+25 so the polynomial can be written as

 

(x-4)(x²+25)=0 and x=4 and x=5i and x=-5i are the roots where i=√-1.

 

Hope this helps

 

Jim