Question

For what value of K is the polynomial p(x)=2x^5 + 3kx^4 - 2x^3- x^2 + x + k divisible by (2x-1).

Answer 1

Answer:

k=-5/19

Step-by-step explanation:

Let 2x-1=0

x= 1/2

p(1/2)= 2(1/2)^5 + 3k(1/2)^4 - (1/2)^2 + 1/2 + k

2(1/32) + 3k(1/16) - 1/4 + 1/2 + k = 0

1/16 + 3k/16 - 1/4 + 1/2 + k = 0

3k/16 + k = 1/4 -1/2 - 1/16

3k + 16k / 16 = 4 - 8 -1 / 16

19k = -5

k = -5 / 19

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