Solving Quadratics with Complex Solutions

Flashcard
•
Mathematics
•
10th - 11th Grade
•
Hard
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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 ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
2.
FLASHCARD QUESTION
Front
What does the discriminant (b² - 4ac) indicate in a quadratic equation?
Back
The discriminant indicates the nature of the roots of the quadratic equation: if > 0, two distinct real solutions; if = 0, one real solution; if < 0, two complex solutions.
3.
FLASHCARD QUESTION
Front
How do you convert a quadratic equation to standard form?
Back
To convert to standard form, rearrange the equation to the form ax² + bx + c = 0.
4.
FLASHCARD QUESTION
Front
Solve for x: 2x² - 3x + 4 = 0
Back
x = {-3+2i, -3-2i}
5.
FLASHCARD QUESTION
Front
What are complex solutions?
Back
Complex solutions are solutions to equations that include imaginary numbers, typically in the form a + bi, where i is the imaginary unit.
6.
FLASHCARD QUESTION
Front
If b² - 4ac < 0, how many solutions does the quadratic equation have?
Back
The quadratic equation has two complex solutions.
7.
FLASHCARD QUESTION
Front
Solve -2x² + 4x = 9
Back
x = (2 - i√14)/2, (2 + i√14)/2
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