College Algebra
Daily Quiz
Evaluate the following:
Name ___KEY____________
1. -3i 5288
1.
-3 .
5288
(-3) ( i ) Divide 5288 or just 88 by 4. The remainder is zero. This corresponds to i0 or i4 ,
both which equal 1.
(-3)(1) = -3
Solve, using the indicated method. You must show the work to get credit:
2
2. 2x – 8x + 8 = 0 (factor)
2. x = 2, double root
GCF is 2. 2(x 2  4x  4)  0 . Factor (x 2  4x  4)  0 into
6
2 17

, which reduces to :  3  17 . Set each factor = 0.
2
2
2  0. (x  2)2 means (x – 2)(x – 2). x – 2 = 0 gives x = 2, which is a double root, which
means you have 2 identical roots.
2
3. x   3  17
3. x + 6x – 8 = 0 (complete the square)
C. S. has to be = the constant. Adding 8 to both sides results in: x2  6x  8 . On the left
side of the equation, 9 completes the square. (6 divided by 2, then the answer, 3, squared).
Add 9 to both sides of the equation, then write the left side as a binomial squared. The
resulting equation is: (x  3)2  8  9 or (x  3)2  17 . Take the square root of both sides.
Don’t forget the  !!! This gives you: (x  3)2   17 or x  3   17 . Subtracting 3
from both sides gives you the final values for x:
x   3  17
2
4. x   3  17
4. x + 6x – 8 = 0 (quadratic formula)
For any equation ax 2  bx  c  0,
b  (b)2  (4ac)
x 
(2a)
(The quadratic formula)
In this problem, a = 1, b = 6, c = -8, which results in: x 
(6)  (6)2  (4  1 ( 8))
=
(2  1)
6  36  ( 32)
6  68
. 68  4  17  2 17
or x 
2
2
6
2 17

, which reduces to :  3  17
Rewrite as:
2
2
x 
NOTE: Number 3 and number 4 are the same problem. They have the
same solutions, even though we used two different methods. This is NOT
a coincidence!