Question

question 30 (mandatory) (1 point)
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) $b^2 - 4ac \
eq 0$

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

Explanation:

Step1: Recall Discriminant Rules

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

• If \(D > 0\): Two distinct real roots (x - intercepts).
• If \(D = 0\): One real root (x - intercept, a repeated root).
• If \(D < 0\): No real roots (no x - intercepts, since roots are complex).

Step2: Match with the Question

The question asks for the discriminant where there are no real solutions and no x - intercepts. From the rules, this happens when \(b^2 - 4ac < 0\).

Answer:

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