Solving by the Quadratic Formula Quadratic Formula You
Solving by the Quadratic Formula
Quadratic Formula You must have a QUADRATIC before solving!
Steps to simplify: 1. Make sure each variable is in parenthesis. 2. Solve for the discriminant. JUST the part UNDER the radical. 3. Split up the fractions. 4. Simplify each fraction.
Example A:
Example B:
Practice: 1) 2) 3)
IRRATIONAL How do I find the x-intercepts of a polynomial equation that will not factor?
IRRATIONAL ROOTS This will occur when you get a polynomial Might need to use the Quadratic Formula: after synthetic division that CANNOT be factored! But you MUST get it down to a quadratic!
What if it doesn’t factor to begin with or you aren’t sure? � Find a root to begin synthetic division using your calculator, and get it down to a quadratic! f(x) = x 4 + 3 x 3 – 5 x 2 – 15 x 0 1 -3 1 1 3 -5 0 -15 -3 0 15 0 -5 0 0 3 -15 0 0 0 x = 0 , -3
(-3 and 1 using the calculator) Find all of the roots of: g(x) = x 4 + 2 x 3 – 5 x 2 – 4 x + 6 ANSWER: -3, 1, ,
Find all of the roots of: (x=3 using the calculator) g(x) = 4 x 3 – 16 x 2 + 11 x + 3 ANSWER: 3, ,
Find all of the zeros of: (x=4 using the calculator) g(x) = 3 x 3 – 22 x 2 + 32 x + 32 ANSWER: 4, 4 ,
Find all of the roots of: (x=-3 using the calculator) g(x) = x 3 – x 2 – 11 x + 3 ANSWER: -3, ,
Homework!! Work and sketch on a separate piece of paper.
- Slides: 14