Question

Find K, if x-2 is a factor of x^3-2Kx^2+Kx-1.

Answer 1

( X - 2 ) is a factor of the given polynomial X³ - 2KX² + KX - 1.

So,

( X - 2 ) = 0

X = 2

P ( X ) = X³ - 2KX² + KX - 1

P (2) = (2)³ - 2K × (2)² + K × 2 - 1

=> 8 - 2K × 4 + 2K - 1 = 0

=> - 8K + 2K + 7 = 0

=> -6K = -7

=> K = 7/6

Answer 2

Heres your answer

By using Factor Theorem

$p(2) = {2}^{3} - 2k {2}^{2} + 2k - 1 \\ \\ = 8 - 8k + 2k - 1 \\ \\ - 6k = - 8 +1 \\ \\ - 6k = - 7 \\ \\ - k = \frac{ - 7}{ - 6} \\ \\ - k = \frac{ - 7}{6} \\ \\ k = \frac{7}{6}$


Hope it Helps !!