6

Set 14: Quadratic Equations (Advanced)

Explanation

Answer: A

If a line intersects a parabola at two points, the discriminant of the resulting quadratic equation is:

A.

Positive

✓ Correct
B.

Zero

C.

Negative

D.

Undefined

Detailed Explanation

Choice A is correct. Choice A is the correct answer. When solving a system of a linear and quadratic equation, you get a new quadratic equation. * 2 Intersections \leftrightarrow 2 Real Solutions \leftrightarrow Positive Discriminant. * 1 Intersection (Tangent) \leftrightarrow 1 Real Solution \leftrightarrow Zero Discriminant. * 0 Intersections \leftrightarrow No Real Solutions \leftrightarrow Negative Discriminant. Choice B is incorrect because zero means 1 point (tangent). Choice C is incorrect because negative means 0 points. Choice D is incorrect.

Key Steps:

The correct answer is Positive

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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