TEST 9: Complex numbers, the roots of quadratic equations

MQ5 home    Test 8    Test 10

MQ5 TEST 9A (answers below)                                                                              Mr. Gary Jaye

INSTRUCTIONS: 1. TWO-Sided test paper.
                                2. Express all answers in simplest form and SHOW WORK when not asked to fill in.

In 1 to 6, simplify the expression. [3 each]

1.  
 		 2.  3.  
4.  5.   6. 

 

In 7 to 11, fill in the answers. (Hint: use calculator) [3 each]

EQUATION

Discriminant

# of Distinct Roots

Nature of Roots

7. 2x2 + 3x 9 = 0      
8. 4x2 - 20x + 25 = 0      
9. 2x2 - 3x + 8 = 0      
10. 6x2 + 11x - 10 = 0      
11.       

 

12. Form a quadratic equation with integral coefficients whose roots are        [6] 

 
13 and 14 refer to the Gaussian plane. [2 each]  15 and 16 refer to 7x2 - 56x + 19 = 0 . [2 each] 
13. The graph of   lies in Quadrant ??? 
 
 		 15. Find the sum of the roots. 
 
 
 
14. Find  
 		 16. Find the product of the roots. 
 
In 17a. and 18a,  is given.                               [3 each] 
17a. Solve for x. 
 		 18a. Solve for y. 
 
In 17b and 18b,  3x2 + kx - 24 = 0; r1 = 4 / 3 is given.                       [3 each] 
17b. Use the sum or product formula to solve for r2.  18b. Use the sum or product formula to solve for k. 
In 19 and 20, x2 - 6x + k = 0 is given.   [3 each] 
19. Find the value(s) of k for which the equation has one real   double root. 
 
 		 20. Solve the equation with the value of k found in #19. 

 
21. Find the value(s) of k for which 2x2 + x + k = 0 has two distinct real roots. [3] 
 
 		 22. Find the value(s) of k for which x2 + kx + 9 = 0 has imaginary roots.    [3] 
 
 

23. Factor over C: 1 - 16x4            [4]
 


24. Express  as a single complex number in standard form.     [7]
 


25. Express the quotient of  in standard form.      [8]
 
 

ANSWERS: 1. -i  2. -i  3. i  4. -i/2  5. -5(3Ö7)  6. 3/34 - (5/34)i   7. (81, 2, real and rational)
8. (0, 1, real and rational) 9. (-55, 2, imaginary)  10. (361, 2, real and rational)  11. (0, 1, real and irrational!!!)
12. 4x2 - 4x + 13 = 0  13. Q. III   14. 13  15. 8  16. 19/7  17a. x = -4  18a. y = 2  17b. r = 6  18b. k = -14
19. k = 9  20. {3}  21. {k: k < 1/8}  22. {k: -6 < k < 6} 23. (1 + 2ix)(1 - 2ix)(1 + 2x)(1 -  2x)
24. 21/25 - (6/25)i  25. -1/5 + (2Ö6/5)i

MQ5 home    Test 8   Test 10