Question

The graph of a quadratic function intercepts the x-axis in the two places and the y-axis in one place. According to the fundamental theorem of algebra, which of the following statements is correct? The quadratic function has no real zeros and two non-real zeros. The quadratic function has two distinct real zeros and one distinct non-real zero. The quadratic function has two distinct real zeros. The quadratic function has one distinct real zero and one distinct non-real zero.

Answer 1

The best answer is The quadratic function has two distinct real zeros

The fundamental theorem of Algebra basically states that a the number of zeros, or roots, that a function has will be equal to the degree of the polynomial. In this case, the functions degree is two since it is a quadratic function, so there should be two roots. The roots can be real or non-real. 

In this case, based on the fact that two roots cross the x-axis and are apparently part of the continuous function, both roots are distinct and real. 
If one or two were imaginary, we would not see them in the graph of the function. 

Answer 2

Answer:

B.

The quadratic function has two distinct complex zeros.