Question

question 20 (mandatory) (1 point)
which discriminant indicates that a quadratic function has two distinct real solutions and the function has two x-intercepts?

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

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

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

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

Explanation:

Step1: Recall discriminant rules

For a quadratic equation \(ax^2 + bx + c = 0\) (\(a
eq0\)), the discriminant is \(D = b^2 - 4ac\).

• If \(D < 0\): No real solutions (no x - intercepts).
• If \(D = 0\): One real solution (one x - intercept, a repeated root).
• If \(D>0\): Two distinct real solutions (two x - intercepts).
• \(D

eq0\) means either \(D > 0\) or \(D < 0\), but we need two distinct real solutions (so \(D>0\)).

Step2: Analyze each option

• Option a: \(b^2 - 4ac<0\) means no real solutions, so incorrect.
• Option b: \(b^2 - 4ac

eq0\) means either \(>0\) or \(<0\). If \(<0\), no real solutions, so not specific for two distinct real solutions. Incorrect.

• Option c: \(b^2 - 4ac > 0\) means two distinct real solutions (and two x - intercepts). Correct.
• Option d: \(b^2 - 4ac = 0\) means one real solution (one x - intercept). Incorrect.

Answer:

c) \(b^2 - 4ac > 0\)