The discriminant
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the discriminant in a quadratic equation?
Back
The discriminant is the expression b² - 4ac in the quadratic formula ax² + bx + c = 0.
2.
FLASHCARD QUESTION
Front
What does a positive discriminant indicate about the solutions of a quadratic equation?
Back
A positive discriminant indicates that there are two distinct real solutions.
3.
FLASHCARD QUESTION
Front
What does a negative discriminant indicate about the solutions of a quadratic equation?
Back
A negative discriminant indicates that there are no real solutions, only complex solutions.
4.
FLASHCARD QUESTION
Front
What does a zero discriminant indicate about the solutions of a quadratic equation?
Back
A zero discriminant indicates that there is exactly one real solution, also known as a repeated or double root.
5.
FLASHCARD QUESTION
Front
How do you calculate the discriminant for the quadratic equation 3x² + 2x - 1 = 0?
Back
The discriminant is calculated as b² - 4ac = (2)² - 4(3)(-1) = 4 + 12 = 16.
6.
FLASHCARD QUESTION
Front
If the discriminant of a quadratic equation is 0, what can be said about its graph?
Back
The graph of the quadratic equation touches the x-axis at one point (the vertex) and does not cross it.
7.
FLASHCARD QUESTION
Front
What is the significance of the discriminant in determining the nature of the roots of a quadratic equation?
Back
The discriminant helps determine whether the roots are real and distinct, real and equal, or complex.
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