Transcription of Finding Rational Zeros - ClassZone
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Finding Rational Zeros - ClassZone
Page 1 of 2. Finding Rational Zeros GOAL 1 USING THE Rational zero THEOREM. What you should learn GOAL 1 Find the Rational The polynomial function Zeros of a polynomial function. (x) = 64x 3 + 120x 2 34x 105. 3 5 7. GOAL 2 Use polynomial has , , and as its Zeros . Notice that the numerators of these Zeros ( 3, 5, 2 4 8. equations to solve real-life and 7) are factors of the constant term, 105. Also notice that the denominators (2, 4, problems, such as Finding the dimensions of a monument and 8) are factors of the leading coefficient, 64. These observations are generalized in Ex. 60. by the Rational zero theorem. Why you should learn it T H E R AT I O N A L Z E R O T H E O R E M. To model real-life quantities, such as the If (x) = an x n + .. + a1x + a0 has integer coefficients, then every Rational zero volume of a representation of has the following form: of the Louvre pyramid in Example 3. AL LI p factor of constant term a0. = . FE. RE. q factor of leading coefficient an EXAMPLE 1 Using the Rational zero Theorem Find the Rational Zeros of (x) = x 3 + 2x 2 11x 12.
Page 1 of 2 6.6 Finding Rational Zeros 359 Finding Rational Zeros USING THE RATIONAL ZERO THEOREM The polynomial function ƒ(x) = 64x3+ 120x2º 34x º105has º3 2, º5 4, and 7 8 as its zeros. Notice that the numerators of these zeros (º3, º5,
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