Question

If k is the zero of the polynomial x6 - kx5+2x4-2kx3+3x-k+2 then find the value of k

Answer 1

if  k is zero of polynomial
then x=k is substituted
k^6 -k^6+2k^4-2k^4+3k-k+2=0
2k+2=0
k=-1

Answer 2

Here is your answer

k is a factor of polynomial kx^5 + 2x⁴ - 2kx³ + 3x - k + 2


put x= k in polynomial kx5 + 2x4 - 2kx³ + 3x - k + 2.


k × (k)^5 + 2 × (k)⁴ - 2k × (k)³ + 3k - k + 2
k^6 + 2k⁴ - 2k⁴ + 2k + 2 = 0
k^6 + 2k + 2 =0
k ( k^5 + 2 ) = -2
k × k^ 5 + 2 = -2
k = 0

Hope it helps you ^_^