Question

if \\(x = 6\\) is the only \\(x\\)-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

the discriminant is 0
the discriminant is 6
the discriminant is positive
the discriminant is negative

Explanation:

Relate x-intercepts to real roots

$$ \text{Number of } x\text{-intercepts} = \text{Number of unique real roots} = 1 $$

Determine the discriminant value for one real root

$$
LATEXBLOCK0
$$

$$ \therefore D = 0 $$

Answer:

• The discriminant is 0 (Correct answer)
• The discriminant is 6
• The discriminant is positive
• The discriminant is negative