Use the fundamental theorem of algebra to determine the number of roots for 2x^2+4x+7
what are the roots of 2x^2+4x+7
show work, i cant learn anything if i just get the answer.

The fundamental theorem of algebra says that a th degree polynomial will have up to distinct complex roots.

the degree for this polynomial is , so there are up to two distinct roots.

we can find more specific information about the roots by checking the sign of the discriminant. for , the discriminant is the quantity , which in this case would be . because the discriminant is negative, there are two complex (non-real) roots.