Question

Find the value of k if x-3 is a factor of k square X cube - Kx square +3kx-k

Answer 1

Solution:

Let p(x) = k²x³-kx²+3kx-k

If (x-3) is a factor of p(x), then

p(3) = 0

=> k²(3)³-k(3)²+3k*3-3 = 0

=> 3[ 9k²-9k+3k-3] = 0

=> 9k²-6k-3 = 0

Splitting the middle term, we get

=> 9k² -9k +3k - 3 = 0

=> 9k(k-1)+3(k-1) = 0

=> (k-1)(9k+3) = 0

=> k-1 = 0 or 9k+3 = 0

=> k = 1 or 9k = -3

=> k = 1 or k = -3/9

=> k = 1 or k = -1/3

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