3

I fully answered the question, and got that $k=-3$, but the answer says it's positive. Can anyone show me my mistake?

"Given that $x-2$ is a factor of the polynomial $x^3 - kx^2 - 24x + 28$, find $k$ and the roots of this polynomial."

Using factor theorem, I realised that $P(2)$ is equivalent to $0$, therefore $2^3 - 2^2k - 24(2) + 28 = 0$

I solved it algebraically and got that $k=-3$, but the answers say it was $k=3$. Did I make a simple error?

Any help would be appreciated.

missiledragon
  • 605
  • 9
  • 23

2 Answers2

4

No error on your part:

If you've copied the problem correctly, then your solution is correct: $k = -3$.

I was very careful in calculating, as I'm sure you were, in double checking, so if $(x - 2)$ is a factor for your given polynomial, then $k$ must be $-3$.

Typo/misprint I suspect, in your text: a typo in the solution, or a misprint of the desired polynomial.

E.g. If the polynomial had been

$$x^3 \color{blue}{\large \bf +} 4k^2 - 24x + 28\quad \text{and}\;\; (x-2) \;\text{is a factor}$$

then $k = 3$.

amWhy
  • 209,954
2

I got k = -3 also. I think the answers may be wrong:

2 | 1     -k      -24           28
  |        2      2(-k + 2)     4(-k + 2)-48
  |____________________________________________
    1   (-k + 2)  2(-k + 2)-24  4(-k + 2)-48+28

-4k+8-48+28 = 0
-4k = 12
k = -3
Ace
  • 63