Question

If x+2k is a factor of f(x)=x5-4k2x3+2x+2k+3,find k

Answer 1

Let p(x) = x5 − 4k2x3 + 2x + 2k + 3

Given (x + 2k) is a factor of p(x)

Hence p(−2k) = 0 by remainder theorem

Put x = −2k in p(x)

p(−2k) = (−2k)5 − 4k2(−2k)3 + 2(−2k) + 2k + 3

0 = −32k5 − 4k2(−8k3) − 4k + 2k + 3

⇒ −32k5 + 32k5 − 2k + 3 = 0

⇒ − 2k + 3 = 0

⇒ 2k = 3

∴ k = (3/2)

Answer 2

Answer:

Step-by-step explanation: