# How do you form a polynomial function whose zeros are 3 and 4 + i?

##### 1 Answer

Feb 14, 2016

#### Answer:

Convert zeros to factors and multiply out to find the simplest possible polynomials.

#### Explanation:

If

So the simplest polynomial with these zeros is:

#(x-3)(x-(4+i)) = x^2-(7+i)x+(12+3i)#

If you want Real coefficients, then the Complex conjugate

#(x-3)(x-(4+i))(x-(4-i))#

#=(x-3)((x-4)^2-i^2)#

#=(x-3)(x^2-8x+17)#

#=x^3-11x^2+41x-51#

Any polynomial with these zeros must be a multiple (scalar or polynomial) of these 'simplest' polynomials.