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?

1 The quadratic function has no real zeros and two non-real zeros.
2 The quadratic function has two distinct real zeros and one distinct non-real zero.
3 The quadratic function has two distinct real zeros.
4 The quadratic function has one distinct real zero and one distinct non-real zero.

Answer 1

3: The quadratic function has two distinct real zeros

Answer 2

Correct Answer:
Option 3: The quadratic function has two distinct real zeros.

The function is quadratic, therefore it can have only 2 zeros. The knowledge of x-intercepts is needed to determine the zeros, y-intercepts has nothing to do with the zeros of a function. The given function has 2 unique x-intercepts, so according to the fundamental theorem of algebra, this function has 2 distinct real roots as number of distinct real roots are equal to the number of x-intercepts. Therefore, option 3 is the correct answer.