Question

question 30 (mandatory) (1 point) ✓ saved which discriminant indicates that a quadratic function has no real solutions and the function has no x-intercepts? a) $b^2 - 4ac < 0$ b) $b^2 - 4ac > 0$ c) $b^2 - 4ac ≠ 0$ d) $b^2 - 4ac = 0$

Explanation:

Step1: Recall discriminant rules

For a quadratic \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\).

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

Step2: Match with options

We need discriminant for no real solutions (no x - intercepts), so \(b^2 - 4ac < 0\) (option a).

Answer:

a) \(b^2 - 4ac < 0\)