Math
posted by Paul on .
Find a polynomial of degree 3 with roots 3, 4  i.
Which one is it?
A.x3  10x + 15
B.x3 + 15x2 + 4x  50
C.x3  11x2 + 41x  51
D.x3 + 24x2 + 3x  12

Well, 3 is a root of C, and the others are not.
See if Google calculator can do the other root; paste this into the google search engine window:
(4i)^311(4i)^2 +41(4i)51 
They all are degree 3.
See if x=3 works for each choice. It does not work for A, B or D.
If one of the choices is correct, it must be (C)
If you want to see if 4i is a root, longdivide polynomial (C) by (x3) and see what the roots are for the remaining quadratic, which is
x^2 8x +17 = 0.
x = (1/2) [8 +/ sqrt(4)]
= 4 +/ i 
3, 4i then also 4+i
(x3)(x4+i)(x4i) = 0
(x3)(x^2  8x + 17)
x^3  11 x^2 + 41 x  51 
Hello Damon im not understanding... are you saying the answer is c?

We are all saying the answer is C.

X=3, X3=0. X=4i, x4=i, Square both
sides:X^28X+16=1,X^28X+17=0, Multiply:(X3)(X^28X+17)=0
X^311X^2+41X51=0.
Yes, the correct choice is C.