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Transcript
Name: ________________________ Class: ___________________ Date: __________ ID: A Algebra II Honors Test Review 6-5 to 6-6 Short Answer 1. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x 3 − 10x 2 + 5x − 2 = 0. Do not find the actual roots. 2. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x 3 + x 2 − 7x − 4 = 0. Do not find the actual roots. 3. Find the rational roots of x 4 + 8x 3 + 7x 2 − 40x − 60 = 0. 4. A polynomial equation with rational coefficients has the roots 1 + 7, 2 − 6 . Find two additional roots. 5. Find a third-degree polynomial equation with rational coefficients that has roots –4 and 3 + i. For the equation, find the number of complex roots, the possible number of real roots, and the possible rational roots. 6. x 7 − 2x 6 + 3x 2 − 2x + 5 = 0 7. 10x 7 − 10x 6 + 4 = 0 1 Name: ________________________ ID: A Find the roots of the polynomial equation. 8. 4x 3 + 16x 2 − 22x − 10 = 0 9. x 3 − 2x 2 + 10x + 136 = 0 10. x 4 − 5x 3 + 11x 2 − 25x + 30 = 0 11. Find all zeros of 2x 4 − 3x 3 + 30x 2 − 48x − 32 = 0. 12. Find all zeros of 2x 4 − 5x 3 + 53x 2 − 125x + 75 = 0. 2 ID: A Algebra II Honors Test Review 6-5 to 6-6 Answer Section SHORT ANSWER 1. –2, –1, 1, 2 2. –4, –2, –1, 1, 2, 4 3. –6, –2 4. 1 − 7, 2 + 6 5. x 3 − 2x 2 − 14x + 40 = 0 6. 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ±5 7. 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ± 2, ± 4, ± 8. −5, 1± 3 2 9. 3 ± 5i, –4 10. 2, 3, ± i 5 1 11. 2, − , ± 4i 2 3 12. 1, , ± 5i 2 1 1 1 2 4 1 , ± , ± , ± , ± 2 5 5 5 10