If #kx^3-kx+9# is divisible by #x-1#, then what is #k#?

1 Answer
George C.
Feb 13, 2018

#k = 1/2+-sqrt(35)/2i#

Explanation:

Given:

#f(x) = k^2x^3-kx+9#

If #f(x)# is divisible by #(x-1)# then #f(1) = 0#, so:

#0 = f(1) = k^2-k+9#

Solving for #k# using the quadratic formula we find:

#k = (1+-sqrt((-1)^2-4(1)(9)))/(2(1))#

#color(white)(k) = (1+-sqrt(1-36))/2#

#color(white)(k) = 1/2+-sqrt(35)/2i#

Related questions
Impact of this question
1352 views around the world
You can reuse this answer
Creative Commons License