FUNCTIONS 1

If f(x) = x⁴ + kx² + 6x + 7 has a remainder of 10 when divided by x+2; find k.

Solution

f(x) = x⁴ + kx² + 6x + 7

x + 2 = 0

x = -2

f(x) = (-2)⁴ + k(-2)² + 6(-2) + 7 = 10

16 + 4k + (-12) + 7 = 10

16 + 4k - 12 + 7 = 10

16 + 4k - 5 = 10

4k + 16 - 5 = 10

4k + 11= 10

4k = 10 - 11

4k = -1

4k = -1

4      4

k = ^-1/4

hence k= ^-1/4

TRY THIS......................

  

If f(x) = x⁴ - kx² + 2x - 1 has a remainder of 18 when divided by x-3; find k.