Question

A={x:x belongs to N, G.C.D.(x,36) = 1, x < 36}, B={y:y belongs to N, G.C.D.(y,40) = 1, y < 40} find, n(A intersection B); C={x:x belongs to A Union B, x is prime},N(C); n (A-B)union( B-A); and n((A-B) ×(B-A)).

Answer 1

x = -2 is root of √2(x+p) = 0
substituting value of x:
√2(p-2) = 0
√2p - 2√2 = 0
√2p = 2√2
p = 2 ___ (i)

-2 is zero of px² + kx + 2√2
therefore 2(-2)² + k(-2) + 2√2 = 0
8 - 2k + 2√2 = 0
4 - k + √2 = 0
k = 4 + √2

Hope This Helps :)