Roots of Quadratics

Flashcard
•
Mathematics
•
12th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a quadratic equation?
Back
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
2.
FLASHCARD QUESTION
Front
What is the discriminant of a quadratic equation?
Back
The discriminant is the part of the quadratic formula under the square root, given by D = b^2 - 4ac. It determines the nature of the roots.
Tags
CCSS.HSA-REI.B.4B
3.
FLASHCARD QUESTION
Front
What does a positive discriminant indicate?
Back
A positive discriminant indicates that the quadratic equation has two distinct real roots.
Tags
CCSS.HSA-REI.B.4B
4.
FLASHCARD QUESTION
Front
What does a discriminant of zero indicate?
Back
A discriminant of zero indicates that the quadratic equation has exactly one real root (a repeated root).
Tags
CCSS.HSA-REI.B.4B
5.
FLASHCARD QUESTION
Front
What does a negative discriminant indicate?
Back
A negative discriminant indicates that the quadratic equation has two complex (non-real) roots.
Tags
CCSS.HSA-REI.B.4B
6.
FLASHCARD QUESTION
Front
Calculate the discriminant for the equation 3x^2 - 2x + 1 = 0.
Back
D = (-2)^2 - 4(3)(1) = 4 - 12 = -8 (Complex roots).
Tags
CCSS.HSA-REI.B.4B
7.
FLASHCARD QUESTION
Front
Calculate the discriminant for the equation x^2 - 4x + 4 = 0.
Back
D = (-4)^2 - 4(1)(4) = 16 - 16 = 0 (One real root).
Tags
CCSS.HSA-REI.B.4B
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