A4x4 matrix a with real entries and a4 = i, what are the possible characteristic polynomials of a

If , then the characteristic polynomial of is



which means has eigenvalues .

We know that if is an eigenvalue of , then is an eigenvalues of .

So if is the only eigenvalue of , we know that are the only possible eigenvalues of . We can construct five possible characteristic polynomials for in that case.

Answer to your question: a. the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. the roots are ​ x=1±i7√2 .number of roots=degree of polynomialhere, degree of polynomial is 2 so number of roots will be 2.hope it *_*