Quadratic Formula and Discriminant

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•
Mathematics
•
8th - 9th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the quadratic formula?
Back
The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).
2.
FLASHCARD QUESTION
Front
What does the discriminant tell us about a quadratic equation?
Back
The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation. If D > 0, there are 2 real solutions; D = 0 means 1 real solution; D < 0 indicates no real solutions.
3.
FLASHCARD QUESTION
Front
If the discriminant is positive, how many solutions does the quadratic equation have?
Back
2 real solutions.
4.
FLASHCARD QUESTION
Front
If the discriminant is zero, how many solutions does the quadratic equation have?
Back
1 real solution.
5.
FLASHCARD QUESTION
Front
If the discriminant is negative, how many solutions does the quadratic equation have?
Back
No real solutions.
6.
FLASHCARD QUESTION
Front
Solve using the quadratic formula: x² - 4x - 5 = 0
Back
x = 5, x = -1.
7.
FLASHCARD QUESTION
Front
What is the value of the discriminant for the equation 3x² + 6x + 2 = 0?
Back
D = 6² - 4(3)(2) = 36 - 24 = 12 (positive, so 2 real solutions).
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