# Thread: Constucting cubic function from given complex zeros.

1. ## Constucting cubic function from given complex zeros.

Hi, The question is Write down a polynomial of degree 3, whose coefficients are all real, that has 4i and 2 as two of its zeros.

2. If you are asked to write down , for example, a polynominal of degree 2 that has 2 and 3 as its zeros, you will find;
f(x) = (x-2)(x-3)
by substituting either x=2 or x=3, it's clear this satisfies the question.

Similarly,....

+ if an polynominal f(x)=0 <whose coefficient is all real> has an complex root, x = a+bi, (a and b are real), we can say...

3. Originally Posted by Barney
Hi, The question is Write down a polynomial of degree 3, whose coefficients are all real, that has 4i and 2 as two of its zeros.

$(x-2)(x-4i)(x+4i)=0$