Question

The graph of a quadratic function does not cross the x-axis, but crosses the y-axis in one place.
According to the fundamental theorem of algebra, which of the following statements is correct?

A.
The quadratic function has two distinct real zeros.
B.
The quadratic function has no real zeros and one distinct complex zero.
C.
The quadratic function has one distinct real zero and one distinct complex zero.
D.
The quadratic function has two distinct complex zeros.

Answer 1

Answer: D

Step-by-step explanation:

A quadratic function has a degree of 2 so there will be two roots.  The statement says the function does NOT CROSS THE X-AXIS so there are no real roots. That means both roots must be imaginary (complex).

Answer 2

According to the Fundamental Theorem of Algebra, the correction statement is:

"The quadratic function has two distinct complex zeros." (Option D)

What is the Fundamental Theorem of Algebra?

The Fundamental Theorem of Algebra states that every polynomial equation of degree 'n' with complex number coefficients has 'n' roots, or solutions, in the complex numbers.

For example, the polynomial x^4 + 3x^2 - 6x - 8 has a degree of 4 because its largest exponent is 4.

Recall that there are no complex roots with a quadratic function because its roots do not go beyond 2.

Learn more about the Fundamental Theorem of Allegra at:
https://brainly.com/question/10345879