Help
Options
Didn't know it?
click below
click below
Knew it?
click below
click below
Don't Know
Remaining cards (0)
Know
retry
shuffle
restart
0:00
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
Quadratic
| Question | |
|---|---|
| Quadratic formula | x = (−b ± √(b² − 4ac)) / 2a |
| Discriminant | D = b² − 4ac |
| If D > 0 | Roots are real and unequal |
| If D = 0 | Roots are real and equal |
| If D < 0 | Roots are complex and conjugate |
| Sum of roots (α + β) | −b / a |
| Product of roots (αβ) | c / a |
| Quadratic equation from roots α and β | x² − (α + β)x + αβ = 0 |
| If roots are reciprocal | c = a |
| Vertex of parabola | x = −b / (2a) |
| Maximum value of the quadratic expression | = f(−b / 2a) |
| What are the conditions for both roots to be greater than a number k? | The three conditions are: 1. D ≥ 0, 2. -b/2a > k, and 3. a × f(k) > 0. |
| What are the conditions for both roots to be less than a number k? | : The three conditions are: 1. D ≥ 0, 2. -b/2a < k, and 3. a × f(k) > 0 |
| What is the condition for a number k to lie between the two roots? | The single condition is a × f(k) < 0 |
| What are the conditions for both roots to lie between two numbers k₁ and k₂? | The three conditions are: 1. D ≥ 0, 2. k₁ < -b/2a < k₂, and 3. a × f(k₁) > 0 and a × f(k₂) > 0. |
| What is the condition for exactly one root to lie between two numbers k₁ and k₂? | The single condition is f(k₁) × f(k₂) < 0 |
| general cubic Sum of roots α+β+γ | =-b/a |
| Sum of products of roots (taken two at a time) αβ+βγ+γα | = c/a |
| Product of roots αβγ | = d/a |
| absolute difference between its two roots |x1 - x2| is given by | |x₁ - x₂| = b^2 - 4ac / |a| |
| If roots of a quadratic equations are rational then discriminant must be a? | perfect square |
| If a quadratic is greater than zero than is discriminant ? | less than zero |
| If a quadratic is greater than and equal to zero than is discriminant ? | less than or equal to zero |
| Minimum value of a Quadratic equation | -D/4a |
Created by:
rajat 1234545