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Notes 6.6 Fundamental Theorem of Algebra
If P(x) is a polynomial with degree n >1 with complex coefficients, then P(x) = 0 has at least one complex root.
An nth degree polynomial equation has exactly n roots; related polynomial function has exactly n zeros. If you factor a polynomial of degree n, then it has n linear factors.
EX 1 x4 – 3x3 + 4x + 1 = 0 State the number of complex roots, the possible number of real roots, and the possible rational roots.
EX 2 State the number of complex roots, the possible number of real roots, and the possible rational roots. x3 + 2x2 – 4x – 6 = 0
EX 3 Find all the zeros. x5 + 3x4 – x - 3
4.4 Rational Root Theorem.
Rational Root Theorem.
Zeros of Polynomial Functions Section 2.5. Objectives Use the Factor Theorem to show that x-c is a factor a polynomial. Find all real zeros of a polynomial.
Zeros of Polynomial Functions
Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!
Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Complex Numbers Standard form of a complex number is: a + bi. Every complex polynomial function.
Lesson 2.5 The Fundamental Theorem of Algebra. For f(x) where n > 0, there is at least one zero in the complex number system Complex → real and imaginary.
Warm up Use the Rational Root Theorem to determine the Roots of : x³ – 5x² + 8x – 6 = 0.
General Results for Polynomial Equations
Objectives Fundamental Theorem of Algebra 6-6
Complex Zeros; Fundamental Theorem of Algebra
9.9 The Fundamental Theorem of Algebra
The Rational Root Theorem. Is a useful way to find your initial guess when you are trying to find the zeroes (roots) of the polynomial. THIS IS JUST.
6.6 The Fundamental Theorem of Algebra
7.5 Zeros of Polynomial Functions Objectives: Use the Rational Root Theorem and the Complex Conjugate Root Theorem. Use the Fundamental Theorem to write.
Rational Root and Complex Conjugates Theorem. Rational Root Theorem Used to find possible rational roots (solutions) to a polynomial Possible Roots :
Section 4.3 Zeros of Polynomials. Approximate the Zeros.
General Results for Polynomial Equations In this section, we will state five general theorems about polynomial equations, some of which we have already.
Chapter 2 Polynomial and Rational Functions. Warm Up
2.5 The Fundamental Theorem of Algebra Students will use the fundamental theorem of algebra to determine the number of zeros of a polynomial. Students.
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