algebra study guide 13

complete all questions with solving the problem showing the work and giving the answer

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1. Consider p(x) = x3 − 3×2 − 6x + 8,
(a) (1 point) What is the number of maximum zeros?
(a)
(b) (3 points) Discuss the number of positive, negative, and complex zeros.
Show your answers in the chart (Insert additional rows if needed).
Positive
Solution Types
Negative Complex
Total
(c) (2 points) List all possible rational zeros.
(c)
(d) (3 points) Show that −3 is a lower bound.
(d)
Page 1 of 4
Study Guide 13
Total Points: 50
(e) (4 points) Find all zeros for this polynomial. Express your answer in a solution set.
(e)
2. Consider x4 − 2×3 + 10×2 − 18x + 9 = 0,
(a) (3 points) Discuss the number of positive, negative, and complex zeros.
Show your answers in the chart (Insert additional rows if needed).
Positive
Solution Types
Negative Complex
Total
(b) (2 points) List all possible rational zeros.
(b)
(c) (3 points) Show that 2 is an upper bound.
(c)
Page 2 of 4
Study Guide 13
Total Points: 50
(d) (4 points) Find all zeros including complex zeros if there are any. Express
your answer in a solution set.
(d)
3. Consider p(x) = 2×3 − 3×2 − 8x + 12,
(a) (3 points) Discuss the number of positive, negative, and complex zeros.
Show your answers in the chart (Insert additional rows if needed).
Positive
Solution Types
Negative Complex
Total
(b) (3 points) List all possible rational zeros.
(b)
(c) (3 points) Show that −3 is a lower bound.
(c)
Page 3 of 4
Study Guide 13
Total Points: 50
(d) (4 points) Find all zeros for this polynomial. Express your answer in a solution set.
(d)
4. Consider 4×4 − 21×2 − 25 = 0,
(a) (3 points) Discuss the number of positive, negative, and complex zeros.
Show your answers in the chart (Insert additional rows if needed).
Positive
Solution Types
Negative Complex
Total
(b) (3 points) List all possible rational zeros.
(b)
(c) (3 points) Show that 3 is an upper bound.
(c)
(d) (3 points) Show that −3 is a lower bound.
(d)
Page 4 of 4
Study Guide 13
Total Points: 50

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