The Quadratic Formula and the Discriminant College Algebra
The Quadratic Formula and the Discriminant College Algebra 1. 4 (day 3 Notes)
We have a number of different ways of finding the roots of a quadratic equation #1. Solve by Taking Square Roots #2. Factoring #3. Completing the Square Now a new way that comes from completing the square. The Quadratic Formula
The Quadratic Formula Solve for x by completing the square.
Yes, you can remember this formula Pop goes the Weasel http: //www. youtube. com/watch? v=2 lb. ABbf. U 6 Zc&fe ature=related Gilligan’s Island http: //www. youtube. com/watch? v=3 CWTt 9 QFio. Y&f eature=related This one I can’t explain http: //www. youtube. com/watch? v=haq 6 kp. Wd. EMs& feature=related
How does it work Equation:
How does it work Equation:
The Discriminant The number in the square root of the quadratic formula.
The Discriminant •
The Discriminant can be negative, positive or zero If the Discriminant is positive, there are 2 real answers. If the Discriminant is zero, there is 1 real answer. If the Discriminant is negative, there are 2 complex answers. complex answer have i.
The Discriminant Number of Solutions Type of Solutions Positive, perfect square (ex: 36 or 81 or 100) Two Real and Rational Positive, but not a perfect square (ex: 40, 27, 72, 91, …) Two Real and Irrational Zero One (a double solution) Real and Rational Negative (ex: -49, -81, -5, -27, …) Two Nonreal complex
The Discriminant • This proves that the discriminant is only useful when a, b and c are INTEGERS!!!
Solve using the Quadratic formula
Solve using the Quadratic formula
Solve using the Quadratic formula
Solve using the Quadratic formula
Solve using the Quadratic formula
Solve using the Quadratic formula
Solve using the Quadratic formula
Solve using the Quadratic formula
Solve using the Quadratic formula
Solve using the Quadratic formula
Solve using the Quadratic formula
Describe the roots Tell me the Discriminant and the type of roots
Describe the roots Tell me the Discriminant and the type of roots 0, One rational root
Describe the roots Tell me the Discriminant and the type of roots 0, One rational root
Describe the roots Tell me the Discriminant and the type of roots 0, One rational root -11, Two complex roots
Describe the roots Tell me the Discriminant and the type of roots 0, One rational root -11, Two complex roots
Describe the roots Tell me the Discriminant and the type of roots 0, One rational root -11, Two complex roots 80, Two irrational roots
Homework 1. 4 #72 -82 even and 83 -91 all
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