Question

Which of the following statements about the discriminant (D) of function h, which has an x-intercept at (4,0), must be true?

A) D ≥ 0
B) D > 0
C) D = 0
D) D < 0

Answer 1

The correct statement about the discriminant of function h, which has an x-intercept at (4,0), is A) D ≥ 0, implying that the function has at least one real x-intercept.

Step-by-step explanation:

The discriminant (D) is a component of the quadratic formula and is used to determine the nature of the roots of a quadratic equation. When a function has an x-intercept, such as the function h with an x-intercept at (4,0), it means that the function touches or intersects the x-axis at that point. Since an x-intercept indicates a real root, the discriminant must be zero or positive because negative discriminants correspond to complex roots which do not intersect the x-axis.

Therefore, the correct statement about the discriminant of the function h is A) D ≥ 0, which indicates that the discriminant is zero or positive, signifying that the function has at least one real x-intercept.