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7.5 Zeros of Polynomial Functions
Objectives: Use the Rational Root Theorem and the Complex Conjugate Root Theorem. Use the Fundamental Theorem to write a polynomial function. Standard: N. Solve equations both symbolically and graphically.
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The Rational Root Theorem can be used to identify possible roots of
polynomial equations with integer coefficients. Rational Root Theorem Let P be a polynomial function with integer coefficients in standard form. If p/q (in lowest terms) is a root of P(x) = 0, then p is a factor of the constant term of P and q is a factor of the leading coefficient of P.
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* 8x3 + 10x2 - 11x + 2 = 0
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* Q(x) = x3 - 6x2 + 7x + 2
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* Q(x) = x3 + 4x2 – 6x – 12
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Ex 3. Find all of the zeros of: Same as above, but you will get an imaginary #.
* P(x) = 3x 3 – 10x x – 4
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* P(x) = x3 - 9x2 + 49x – 145
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* P(x) = -4x 3 + 2x2 – x + 3
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Writing a Polynomial when given the factors:
Write the factored form and standard form of a polynomial equation whose zeros are 3, -3, and 0:
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Complex Conjugate Root Theorem
If P is a polynomial function with real-number coefficients and a + bi (where b ≠ 0) is a root of P(x) = 0, then a – bi is also a root of P(x) = 0.
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PSSA Warm-Up Question Algebra II Chp 7
Standard S Analyze linear, polynomial, and rational functions. How can you identify and describe functions and their graphs? What are the functions zero(s)? 1). Linear Function y = ½x + 2 2). Quadratic Function y = x2 – 2x – 3 3). Cubic Function y = x3 – 4x
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Review of Zeros of Polynomial Functions
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