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Warm-up 11-4. Lesson 11-4 Rational Roots. Objectives Students will: Find roots of polynomials with integer coefficients. x 3 + 2x 2 – 5x + 3 → possible roots are factors of a 0 : ± 1, ± 3 Possibilities change when a n ≠ 1. Rational Root Theorem Roots are a ratio: .
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Lesson 11-4Rational Roots Objectives Students will: Find roots of polynomials with integer coefficients
x3 + 2x2 – 5x + 3 → possible roots are factors of a0 : ± 1, ± 3 Possibilities change when an≠ 1 Rational Root Theorem Roots are a ratio: factors of a0 factors of an We may have fractions!
Testing Possible Roots • Divide: remainder = 0 • Plug in: P(r) = 0 Example 1 P(x) = 3x4 – 11x3 + 10x – 4; find all roots
Example 2 P(x) = 3x3 + 2x2 + 3x + 2; find all roots
Example 3 P(x) = x3 – 3x2 – 8x – 10; find all roots HW 109
