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Activity 32:

Activity 32:. Real Zeros of Polynomials (Section 4.3, pp. 333-340). Rational Zeros Theorem:. If the polynomial has integer coefficients, then every rational zero of P(x) is of the form where p is a factor of the constant coefficient a 0 and q is a factor of the leading coefficient a n.

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Activity 32:

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  1. Activity 32: Real Zeros of Polynomials (Section 4.3, pp. 333-340)

  2. Rational Zeros Theorem: If the polynomial has integer coefficients, then every rational zero of P(x) is of the form where p is a factor of the constant coefficient a0 and q is a factor of the leading coefficient an.

  3. Example 1: List all possible rational zeros of P(x) = 2x4 − x2 − 7. possible rational zeros:

  4. Example 2: Find the real zeros of f(x) = 2x3 − 5x2 − 4x + 3. Write f(x) in factored form and sketch its graph. possible rational zeros:

  5. possible rational zeros: Consequently, we need only factor So -1 is a root which means that

  6. Example 3: Find the real solutions of the equation possible rational zeros:

  7. possible rational zeros:

  8. possible rational zeros: possible rational zeros:

  9. possible rational zeros:

  10. Now we need to find the roots of, x2 – x – 1 Consequently, the real roots of are x = 3, x = – 2 and

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