c) There is c#0 in Zs such that Zs[x]/x2 +3 x +2c is a field. d)x²-3x-4 =0 has no solution in Z₁7 4) Let I) 2x-10 in Z[x] II) 2x-10 in Q[x] III) 2x-10 in Z₁₂[x] One of the following is TRUE a) I & II & III are irreducibles b) Only I & II are irreducibles c) Only I & III are irreducibles d) Only II is irreducible 5) All non-zero divisors in Z[i] are a) {1, -1} ONLY b){1,-1,i,-i} ONLY c) {i, -i} ONLY d) All non-zero elements in Z[i]. 6) One of the following is principal ideal but not prime ideal in Z: a) <29> b) <13> c) <0> d) <21> 7) Given (a+bi) = a² + b² Then the kernel= . :Z[i]Z where b) {0} a) {1,-1} c) {1, -1, i, -i} d) {i, -i} 8)) Let A=[0 -[i], ³= [], [1] · B= Then one of the following is TRUE a) A &B& C are nilpotent in M₂(R) b) A &B are nilpotent in M₂(R) but not C. c) A & C are nilpotent in M₂(R) but not B d) B& C are nilpotent in M₂(R) but not A.