7.5 Zeros of Polynomial Functions

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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 2.8.11.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 2 10x 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 2.8.11 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