Nature of Roots
Introduction
Introduction
When using the quadratic formula, there are 3 types of outcomes as shown in the 3 examples below:
When using the quadratic formula, there are 3 types of outcomes as shown in the 3 examples below:
What determines the nature of the roots? What determines whether an equation has 2 distinct real roots, 2 repeated real roots or no real roots at all?
What determines the nature of the roots? What determines whether an equation has 2 distinct real roots, 2 repeated real roots or no real roots at all?
The answer lies within the radical.
The answer lies within the radical.
It turns out that the discriminant (b² - 4ac) is the determining factor for the nature of roots.
It turns out that the discriminant (b² - 4ac) is the determining factor for the nature of roots.
Computational Thinking Exercise (Quadratic Formula, Discriminant & Nature of Roots)
Computational Thinking Exercise (Quadratic Formula, Discriminant & Nature of Roots)
Try playing with the Python Code for the Quadratic formula under the Flow Chart photo. What would happen to the code if it didn't check for discriminant?
Try playing with the Python Code for the Quadratic formula under the Flow Chart photo. What would happen to the code if it didn't check for discriminant?
You can also explore how the discriminant affects the nature of the roots using the applet below.
You can also explore how the discriminant affects the nature of the roots using the applet below.
Explore it!
Explore it!
The applet below allows you to use the 3 points, A, B and C to construct various quadratic curves. Observe how the discriminant is connected to the nature of the roots for a quadratic curve.
The applet below allows you to use the 3 points, A, B and C to construct various quadratic curves. Observe how the discriminant is connected to the nature of the roots for a quadratic curve.
Summary of Different Cases
Summary of Different Cases
Next: Lets extend our learning by looking at Vieta's Formulas
Next: Lets extend our learning by looking at Vieta's Formulas