question in descri

Question

Write a polynomial of least degree with roots 5 and -1 - 3i 
A) f(x)=x^3-3x^2+5x-50 
B) f(x)= x^3 -3x^2+7x-50 
C) f(x)= x^3-3x^2-50 
D) f(x) = x^3-7x^2-50

Answer 1

roots x = 5, x = -1-3i

 

If -1-3i is a root then so is the complex conjugate -1+3i

 

So we have 3 roots...  x = 5, -1-3i, -1+3i

 

f(x) = (x-5)(x+1+3i)(x+1-3i)

 

...

 

(x+1+3i)(x+1-3i) = x²+x-3ix+x+1-3i+3ix+3i-9i²

 

= x² +2x + 10

 

....

 

f(x) = (x-5)(x²+2x+10)

 

Finish the multiplication and combine like terms to

complete the polynomial