Algebra 2 Problems of the Day

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August 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


1. The function f(x) = (x − 3) / (x² + 2x - 8) is undefined when x equals
1) 2 or − 4
2) 4 or − 2
3) 3, only
4) 2, only

Answer: 1) 2 or − 4
A fraction is undefined when the denominator is equal to zero, so you need to know for what values of x is
(x² + 2x - 8) = 0?
Factor the polynomial into (x + 4)(x - 2) = 0
The zeroes of this equation are -4 and 2, so f(x) is undefined at -4 and 2.

2. Which expression is equivalent to (3k − 2i)², where i is the imaginary unit?
1) 9k² − 4
2) 9k² + 4
3) 9k² − 12ki − 4
4) 9k² − 12ki + 4

Answer: 3) 9k² − 12ki − 4
(3k − 2i)² = (3k - 2i)(3k - 2i) = 9k² - 6ki - 6ki + 4i²
= 9k² - 12ki - 4

3. The roots of the equation x² + 2x + 5 = 0 are
1) -3 and 1
2) -1, only
3) -1 + 2i and -1 - 2i
4) -1 + 4i and -1 - 4i

Answer: 3) -1 + 2i and -1 - 2i
Using the Quadratic Formula, a = 1, b = 2, and c = 5.
The discriminant, b² - 4ac, would be (2)² - 4(1)(5) = 4 - 20 = -16.
This eliminates choices 1 and 2, as a negative discriminant means that there are no real roots to the equation.

x = (-b + (-16)^.5) / (2(a)) = (-2 + 4i ) / (2(1)) = -1 + 2i

Comments and questions welcome.

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