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Questions and Answers
What is a Quadratic Equation?
What is a Quadratic Equation?
- An equation of the form ax² + bx + c = 0, where a ≠0 (correct)
- An equation with a degree higher than 2
- An equation of the form ax + b = 0
- An equation of the form x² + y² = 1
What is the sum of the roots of a quadratic?
What is the sum of the roots of a quadratic?
-b/a
What is the product of the roots of a quadratic?
What is the product of the roots of a quadratic?
c/a
The Quadratic Formula is _____
The Quadratic Formula is _____
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What value completes the square?
What value completes the square?
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What is the Discriminant?
What is the Discriminant?
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Describe the roots if b²-4ac=0.
Describe the roots if b²-4ac=0.
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Describe the roots if b²-4ac>0.
Describe the roots if b²-4ac>0.
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Describe the roots if b²-4ac<0.
Describe the roots if b²-4ac<0.
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Study Notes
Quadratic Equations
- A quadratic equation takes the standard form: ax² + bx + c = 0, with the condition that a ≠0.
Roots of Quadratics
- The sum of the roots of a quadratic equation is given by the formula: -b/a.
- The product of the roots is determined by the formula: c/a.
Quadratic Formula
- The quadratic formula, used to find the roots of a quadratic equation, is not provided but generally is: x = (-b ± √(b² - 4ac)) / (2a).
Completing the Square
- The value needed to complete the square in a quadratic equation is (b/2)².
Discriminant
- The discriminant, denoted as b² - 4ac, is crucial for determining the nature of the roots.
Nature of Roots Based on the Discriminant
- If b² - 4ac = 0, the equation has real, rational, and equal roots.
- If b² - 4ac > 0, the equation has real, unequal roots that can be either rational or irrational.
- If b² - 4ac < 0, the equation has complex, non-real roots.
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