Question

find the value of k where 2x-1 is a factor of 6x²+kx-2

Answer 1

value of k is 1 is correct answer

Answer 2

Given f(x) = 6x^2 + kx - 2.

By Remainder theorem, we get

2x - 1 = 0

2x = 1

x = 1/2.


According to remainder theorem f(1/2) = 0, we get

f(1/2) = 6(1/2)^2 + k(1/2) - 2 = 0

         = 6 * 1/4 + k/2 - 2 = 0

         = 6/4 + k/2 - 2 = 0

         = 6/4 - 2 + k/2 = 0

         = -2/4 + k/2 = 0

         = -1/2 + k/2 = 0

          k/2 = 1/2

             k = 1.


verification:

6(1/2)^2 + 1 * 1/2 - 2 = 0

6/4 + 1/2 - 2 = 0

3/2 - 3/2 = 0

0 = 0


Hope this helps!