1. 3.8 The Discriminant and Imaginary Numbers
Objective:
To use discriminants to determine the nature of the roots of the quadratic equation.
To simplify square roots containing negative radicands.

2. Standard Form of a Quadratic Equation
ax2 + bx + c = 0

3. Quadratic Formula
I will give you the formula, no need to memorize it. However, certain exams, ISAT, PSAT, SAT, ACT might require you have it memorized. Other teachers in the building might require you to memorize it. Keep that in mind.

4. Often abbreviated as “D”
The Discriminant
Often abbreviated as “D”
Quadratic Formula

5. If “D” is a positive perfect square
Nature of the solutions: 2, real, rational
If “D” is a positive non-perfect square
Nature of the solutions: 2, real, irrational
If “D” is zero
Nature of the solutions: 1, real, rational, double root
If “D” is negative
Nature of the solutions: imaginary conjugates

6. Definition of i

7. Definition of i

8. imaginary so

9. Example 3
Simplify

10. Steps for Simplifying Roots
1) Find the largest perfect square that is a factor of the number
2) Write the factor pair under the square root
3) Separate into three square roots
4) We choose a perfect square because we know its square root is an integer.
5) Imply multiplication

11. 1) Find the largest perfect square that is a factor of the number
2) Write the factor pair under the square root
3) Separate into two square roots
4) We choose a perfect square because we know its square root is an integer.
5) Imply multiplication

12. 1) Find the largest perfect square that is a factor of the number
2) Write the factor pair under the square root
3) Separate into two square roots
4) We choose a perfect square because we know its square root is an integer.
5) Imply multiplication

13. You try!

14. You try!

15. Assignment:
3.8 Worksheet