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April 25, 2015

Posted by **Paul** on Wednesday, June 30, 2010 at 7:26pm.

Which one is it?

A.x3 - 10x + 15

B.x3 + 15x2 + 4x - 50

C.x3 - 11x2 + 41x - 51

D.x3 + 24x2 + 3x - 12

- Math -
**bobpursley**, Wednesday, June 30, 2010 at 7:49pmWell, 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:

(4-i)^3-11(4-i)^2 +41(4-i)-51

- Math -
**drwls**, Wednesday, June 30, 2010 at 7:51pmThey 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 4-i is a root, long-divide polynomial (C) by (x-3) 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

- Math -
**Damon**, Wednesday, June 30, 2010 at 7:55pm3, 4-i then also 4+i

(x-3)(x-4+i)(x-4-i) = 0

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

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

- Math -
**Paul**, Wednesday, June 30, 2010 at 8:13pmHello Damon im not understanding... are you saying the answer is c?

- Math -
**drwls**, Wednesday, June 30, 2010 at 8:17pmWe are all saying the answer is C.

- Math -
**Henry**, Wednesday, June 30, 2010 at 9:03pmX=3, X-3=0. X=4-i, x-4=-i, Square both

sides:X^2-8X+16=-1,X^2-8X+17=0, Multiply:(X-3)(X^2-8X+17)=0

X^3-11X^2+41X-51=0.

Yes, the correct choice is C.