Substituting x= -2 in √2(x + p) = 0 , we get
√2(-2 + p) = 0
-2√2 + √2p = 0
√2p = -2√2
p = -2
Substituting p = -2 and x = -2 in
px²+kx+2√2 we get
-2(-2)² + k(-2) +2√2 = 0
-8 - 2k + 2√2 = 0
-2k = - 2√2 + 8
2k = 2√2 - 8
2k = 2(√2 - 4)
=> k = (√2 - 4)