sub x = b and x=-b into the polynomial to obtain 2 equations.
16b^4 -32b^3 +16b^2 +kb -5 = 0
16b^4 +32b^3 +16b^2 -kb -5 = 0
You can then add these 2 equations and find b. (b = +-1/2)
Once you find b, sub it back into the polynomial to find k.
Btw, is this a troung student since this question...