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.

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

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.

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

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

Definition of i

Definition of i

imaginary so

Example 3 Simplify

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

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

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

You try!

You try!

Assignment: 3.8 Worksheet