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Questions and Answers
What is the quadratic formula for solving the equation $ax^2 + bx + c = 0$?
What is the quadratic formula for solving the equation $ax^2 + bx + c = 0$?
- $x = \frac{b \pm \sqrt{b^2 + 4ac}}{2a}
- $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ (correct)
- $x = \frac{b \pm \sqrt{b^2 - 4ac}}{2a}$
- $x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a}$
What is the discriminant of a quadratic equation $ax^2 + bx + c = 0$?
What is the discriminant of a quadratic equation $ax^2 + bx + c = 0$?
- $b^2 + 4ac$
- $b^2 - 4ac$ (correct)
- $-b^2 - 4ac$
- $-b^2 + 4ac$
What is the solution to the quadratic equation $2x^2 - 5x + 2 = 0$ using the quadratic formula?
What is the solution to the quadratic equation $2x^2 - 5x + 2 = 0$ using the quadratic formula?
- $x = \frac{5}{2}, x = 2$
- $x = \frac{1}{2}, x = 2$
- $x = 2, x = \frac{1}{2}$ (correct)
- $x = 2, x = -\frac{1}{2}$
When does the quadratic formula give imaginary roots for a quadratic equation?
When does the quadratic formula give imaginary roots for a quadratic equation?
What is the general form of a quadratic equation?
What is the general form of a quadratic equation?
Flashcards
Quadratic Formula
Quadratic Formula
The quadratic formula is: x = (-b ± √(b² - 4ac)) / 2a; it solves equations of the form ax² + bx + c = 0.
Discriminant
Discriminant
The discriminant is b² - 4ac, found under the square root in the quadratic formula, which determines the nature of the roots.
Solution to 2x² - 5x + 2 = 0
Solution to 2x² - 5x + 2 = 0
The solutions are x = 2 and x = 1/2. Verify by substituting back into the original equation: 2x² - 5x + 2 = 0.
Imaginary Roots Condition
Imaginary Roots Condition
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General Form of Quadratic Equation
General Form of Quadratic Equation
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Study Notes
Quadratic Formula
- The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / 2a
Discriminant of a Quadratic Equation
- The discriminant of a quadratic equation ax^2 + bx + c = 0 is b^2 - 4ac
Solution to a Quadratic Equation
- The solution to the quadratic equation 2x^2 - 5x + 2 = 0 using the quadratic formula is: x = (5 ± √(25 - 16)) / 4
- Simplifying the solution, we get: x = (5 ± √9) / 4, or x = (5 ± 3) / 4
Imaginary Roots
- The quadratic formula gives imaginary roots for a quadratic equation when the discriminant (b^2 - 4ac) is negative
General Form of a Quadratic Equation
- The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠0
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