2. P(x) = x² - x + 1
3. P(x) = 2x² + 4x - 1
4. P(x) = x² - x - 3
5. P(x) = x² +
x + 3/4
6. P(x) = ix² + x - 3
8. P(x) = 2x² - 4x + 2
9. P(x) = x² + (1 - i)x + 2
10. P(x) = x² + 5x + 2
11. P(x) = 2 - x + 3x²
12. P(x) = 2x² + x + 1
MATH 121
THEORY OF POLYNOMIALS
I. A. Use the discriminant to determine whether the zeros are (A) real & equal, (B) real & unequal, or (C) complex.
| 1. P(x) = 3x² + 2x - 3 2. P(x) = x² - x + 1 3. P(x) = 2x² + 4x - 1 4. P(x) = x² - x - 3 5. P(x) = x² + 6. P(x) = ix² + x - 3 |
7. P(x) = x² + 2x + 1 8. P(x) = 2x² - 4x + 2 9. P(x) = x² + (1 - i)x + 2 10. P(x) = x² + 5x + 2 11. P(x) = 2 - x + 3x² 12. P(x) = 2x² + x + 1 |
B. Find the value(s) of k such that the roots have the given properties.
| 13. x² + 5x + k = 0; real and equal 14. 2x² + 3x - k = 0; real and unequal |
15. x² + 2kx + 4 = 0; complex 16. x² + 3kx + 4 = 0 real and unequal |
ANSWERS
| 1) B 2) C 3) B 4) B 5) A 6) Can't tell; coefficients not real 7) A 8) A |
9) Can't tell; coefficients not real 10) B 11) C 12) C 13) 25/4 14) k > -9/8 15) -2 < k < 2 16) k < -4/3 or k > 4/3 |