Question

question 29 (mandatory) (1 point)
which discriminant indicates that a quadratic function has exactly one real solution and the function has one x-intercept?

a) $b^2 - 4ac > 0$

b) $b^2 - 4ac = 0$

c) $b^2 - 4ac < 0$

d) $b^2 - 4ac \
eq 0$

Explanation:

Step1: Recall discriminant rules

For a quadratic \(ax^2 + bx + c\), discriminant \(D = b^2 - 4ac\).

• \(D>0\): 2 real roots (2 x - intercepts).
• \(D = 0\): 1 real root (1 x - intercept, repeated).
• \(D<0\): No real roots (no x - intercepts).

Step2: Match with the problem

The problem needs exactly one real solution (so one x - intercept). From the rules, this happens when \(b^2 - 4ac=0\).

Answer:

b) \(b^2 - 4ac = 0\)