SOLUTION: If x-2 is a factor of f(x)=x^4-5x^2+k, then what is the value of k? when I solved this the answer was -4, but on the choices that was given to us it it's positive 4 a. 4 b. 8

Algebra ->  Volume -> SOLUTION: If x-2 is a factor of f(x)=x^4-5x^2+k, then what is the value of k? when I solved this the answer was -4, but on the choices that was given to us it it's positive 4 a. 4 b. 8       Log On


   

Question 1166349: If x-2 is a factor of f(x)=x^4-5x^2+k, then what is the value of k? when I solved this the answer was -4, but on the choices that was given to us it it's positive 4
a. 4
b. 8
c.10
d.18
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use synthetic division 

        -----------------------
    2  | 1   0  -5   0   k
             2   4  -2  -4
        -----------------------
         1   2  -1  -2   k-4


If is a factor, then 2 is a zero of the function, and if 2 is a zero of the function and is used as the divisor in synthetic division, the remainder must be zero, hence:



John

My calculator said it, I believe it, that settles it


I > Ø

Answer by ikleyn(52920) About Me  (Show Source):
You can put this solution on YOUR website!
.

If  x-2  is the factor of  f(x) = x^4 - 5x^2 + k,

it means that the real number of 2 is the root to this polynomial   (the Remainder theorem).



So we substitute x= 2 into the polynomial and equate it to zero

    f(2) = 2^4 - 5*2^2 + k = 0.


It leads us to

          16 - 5*4 + k = 0

          16 - 20 + k = 0

          -4      + k = 0

          k = 4.      ANSWER

Solved.

See how simple is it ?