How do you write a polynomial function with minimum degree whose zeroes are 5 and 3+2i?

1 Answer
Nov 11, 2017

Answer:

see below

Explanation:

a polynomial#" "P(x)# with minimum degree.

We have the coefficients real, therefore all complex roots occur in conjugate pairs

we have zeros

#x=5=>(x-5)#" "is a factor of #P(x)#

#x=3+3i=>(x-(3+2i))#a factor

#:.x=3-2i=>(x-(3-2i))#a factor

#P(x)=(x-5)(x-(3+2i))(x-(3-2i))#

#P(x)=(x-5)(x^2-x(3-2i)-x(3+2i)+(3+2i)(3-2i))#

#=(x-5)(x^2-3x+cancel(2x i)-3xcancel(-2x i)+9+4)#

#=(x-5)(x^2-6x+13)#

#=x^3-6x^2+13-5x^2+30x-65#

#x^3-11x^2+30x-52#