find the complex zero of polynimial function. write f in factored form f(x)=x^3-10x^2+42x-72

Question

find the complex zero of polynimial function. write f in factored form    f(x)=x^3-10x^2+42x-72

anonymous · Answer

Use the rational zero theorem to find the first zero. So $$a _{n}= 1$$ $$a _{0}=-72$$

So find the factors of $$a _{0}/a _{n}$$ and plug them into the equation to find the first zero. From Descartes"s rule of signs you know that there are 3 possible real zeros or one real zero and two complex zeros.

Since the problem states that there are two complex zeros, then you just need to plug in the positive factors from  $$a _{0}/a _{n}$$ 

You will find that positive 4 is a real zero of the equation. 

So divide f(x)=x^3-10x^2+42x-72 by x-4 

You will get $$x ^{2}-6x+18$$Apply the quadratic equation to this equation to find the two complex zeros.

You should be able to finish now.