Zeros of a Polynomial Fundamental Theorem of Algebra Every complex polynomial function fx( ) of degree n ≥1 has at least one complex zero. The Fundamental Theorem of Algebra tells us that every polynomial can be written as a product of complex linear factors. Find all zeros. Write fx( ) as a product of complex zeros. 1. fx x ( ) = + 2 4 ...

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22. Given that (a + bi)2 = 3 + 4i obtain a pair of simultaneous equations involving a and b. Hence find the two square roots of 3 + 4i. (7) 23. Given that 2 + i is a root of the equation x3 – 6x2 + 13x – 10 = 0 find the other two roots. (5) 24. Given that │z│ = , solve the equation 5z + = 6 – 18i, where z* is the conjugate of z. (7) 25.

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14. Which of the following is the factored form of a 4th degree polynomial function with real coefficients that has = —3, 1, 1 + 5i as zeros? a)f(x) — 15. Write a polynomial of lowest degree with real coefficients and the given zeros. a) Degree: 3 x = 3, 6i b) Degree: 4 x = — , 16.

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This precalculus video tutorial provides a basic introduction into writing polynomial functions with given zeros. It explains how to write polynomial equati...

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The function y 1.4(x 5.6)(x 3.1), given in Example B in your book, is said to be in factored form because it is written as the product of factors. The zeros of the function are the solutions of the equation 1.4(x 5.6)(x 3.1) 0. Example B shows how you can use the zero-product property to find the zeros of the function.

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Writing Polynomial Functions with Specified Zeros 1. Write an equation of a polynomial function of degree 3 which has zeros of 0, 2, and - 5. General solution: Any function of the form where a -0 will have the required zeros.

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Engaging math & science practice! Improve your skills with free problems in 'Solving Word Problems by Finding Zeros Given a Polynomial Function' and thousands of other practice lessons.

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Descartes' rule of sign is used to determine the number of real zeros of a polynomial function. It tells us that the number of positive real zeroes in a polynomial function f (x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients.

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Terminology of Polynomial Functions A polynomial is function that can be written as n f a n x 2 ( ) 0 1 2 Each of the a i constants are called coefficients and can be positive, negative, or zero, and be whole numbers, decimals, or fractions. A term of the polynomial is any one piece of the sum, that is any i a i x. Each individual

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Express the polynomial in the form P(x) = (x - k)Q(x) +r for the given value of k. 9) P(x) = 3x3 - x2 + 2x + 7; k = -1 A) P(x) = (x - 1)·(3x2 + 2x) + 7 B) P(x) = (x + 1)·(3x2 + 2x) + 7

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Worksheet 3.2—Real Zeros of Polynomial Functions Show all work. Give simplified, exact values for all answers. No Calculator is permitted unless specifically stated. I. Multiple Choice 1. Let f be a polynomial function with integer coefficients such that f (30)= . Which of the following statements is not necessarily true?

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Simplifying Polynomials Use the Rational Roots Test to Find All Possible Roots If a polynomial function has integer coefficients , then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient Answer to Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots. write a polynomial function with given roots Input the roots here, separated by comma If you know the roots of a polynomial, its degree and ...

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When two polynomials are divided it is called a rational expression. In such cases you must be careful that the denominator does not equal zero. Division by zero is not defined and thus x may not have a value that allows the denominator to become zero.