Theory of Polynomials

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 + √3x + 3/4

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