 # Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!

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Solving Polynomial Equations

Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!

Rational Root Theorem Used to find possible rational roots (solutions) to a polynomial Possible Roots : P/Q Where P represents the factors of the constant of the polynomial and Q represents the factors of the leading coefficient

Rational Root Theorem

Complex Conjugates Theorem If a + bi is a zero of the polynomial, then a – bi is a zero also. Ex. Find the polynomial whose zeros include 3 and 2 – i

Tricks….. If all the coefficients add to equal 0, then 1 is a root. If the sum of every other coefficient adds to equal the sum of the other every other coefficient, then -1 is a root. Try factoring a cubic by grouping if possible.

Find all solutions and rewrite as a product of factors

Find all solutions and rewrite as a product of factors.

Basic Steps to Follow 1.Factor if possible. 2.Try tricks. 3.“p/q” it. 4.Use synthetic division. 5.At quadratic level, solve either by factoring or by using the quadratic formula.

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