Presentation is loading. Please wait.

Presentation is loading. Please wait.

5.7 Apply the Fundamental Theorem of Algebra

Similar presentations


Presentation on theme: "5.7 Apply the Fundamental Theorem of Algebra"— Presentation transcript:

1 5.7 Apply the Fundamental Theorem of Algebra

2 Fundamental Theorem of Algebra
The degree of the problem identifies the number of solutions to the problem. (Ex) How solutions are there to the problem below? x5 + 2x3 – 5x – 12

3 Write a Polynomial using Zero’s
(Ex) -1, 2, 4 Step 1: Determine the factors that created the zero’s. (x + 1) (x – 2) (x – 4) Step 2: Use Foil Method to simplify the polynomial.

4 Complex Conjugate Theorem
If a + bi is a zero, then a – bi is also a zero. If a + √b is a zero, then a - √b is also a zero.

5 Write a polynomial using the zero’s
(Ex) 3, 2 + √5 Step 1: Write the factors: (x – 3) (x – (2 + √5)) ( x – (2 - √5)) Step 2: Regroup the conjugates: Step 3: Foil Method

6 (Ex) Write a polynomial using the zero’s
4, 1+√5 2, 2i, 4-√6 3, 3 - i

7 HW Problems Write a polynomial using the zero’s. 5, -3, 1 2, 2+√3

8 Discarte’s Rule of Signs
The number of positive real zeros of f is equal to the number of the coefficients of f(x) or is less than this by an even number. The number of negative real zeros of f is equal to the number of the coefficients of f(-x) or is less than this by an even number.

9 Determine the possible number of positive real zeros, negative real zeros, and imaginary zeros.
(Ex) x6 – 2x5 + 3x4 – 10x3 – 6x2 + 8x – 8 Step 1: Determine the number of sign changes. Step 2: Determine how many solutions. Step 3: List the possibilities.

10 Determine the possible amount of positive real zeros, negative real zeros, and imaginary zeros.
(Ex) f(x) = x3 + 2x – 11 (Ex) g(x) = 2x4 – 8x3 + 6x2 – 3x + 1

11


Download ppt "5.7 Apply the Fundamental Theorem of Algebra"

Similar presentations


Ads by Google