Zeros Of Polynomials Worksheet Template With Answer Key - Calin M. Agut (Page 2 of 5) in pdf

Zeros Of Polynomials Worksheet Template With Answer Key - Calin M. Agut Page 2

PreCalculus

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or

irrational.

11) f(x) = x 3 - 2x 2 - 6x + 12

A) 2 (rational), 2 6 (irrational), and -2 6 (irrational)

B) -2 (rational), 6 (irrational), and - 6 (irrational)

C) 2 (rational), 6 (irrational), and - 6 (irrational)

D) 2 (rational), 6 (rational), and -6 (rational)

12) f(x) = x 3 - 7x 2 + 4x + 30

A) 5 (rational), 2 + 7 (irrational), and 2 - 7 (irrational)

B) 5 (rational), 7 (irrational), and - 7 (irrational)

C) 5 (rational), 8 (rational), -6 (rational)

D) 5 (rational), 1 + 7 (irrational), and 1 - 7 (irrational)

13) f(x) = x 3 - 7x 2 + 10x + 6

A) 3 (rational), 2 + 6 (irrational), and 2 - 6 (irrational)

B) 3 (rational), 6 (irrational), and - 6 (irrational)

C) 3 (rational), 1 + 6 (irrational), and 1 - 6 (irrational)

D) 3 (rational), -2 + 6 (irrational), and -2 - 6 (irrational)

Write the polynomial in standard form and identify the zeros of the function.

14) f(x) = (x - 5i)(x +5i)

A) f(x) = x 2 - 25; zeros ± 5i

B) f(x) = x 2 + 5ix + 25; zeros ± 5

C) f(x) = x 2 + 25; zeros ± 5

D) f(x) = x 2 + 25; zeros ± 5i

15) f(x) = (x - 1)(x - 7i)(x + 7i)

A) f(x) = x 3 - x 2 + 49x - 49; zeros 1, ± 7i

B) f(x) = x 3 - x 2 + 7x - 7; zeros 1, ± 7i

C) f(x) = x 3 - x 2 - 7x + 7; zeros 1, ± 7i

D) f(x) = x 3 - x 2 - 7x + 7; zeros -1, ± 7i

16) f(x) = (x + 2)(x + 2)(x + 3i)(x - 3i)

A) f(x) = x 4 + 4x 3 + 13x 2 + 36x + 36; zeros 2 (mult. 2), ± 3i

B) f(x) = x 4 + 4x 3 - 5x 2 - 36x - 36; zeros -2 (mult. 2), ± 3

C) f(x) = x 4 + 4x 3 + 13x 2 + 36x + 36; zeros -2 (mult. 2), ± 3i

D) f(x) = x 4 + 13x 2 + 36; zeros 2 (mult. 2), ± 3

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the

polynomial in standard form.

17) 4i and 3

A) f(x) = x 4 - 13x 2 - 48

B) f(x) = x 4 - 26x 2 + 48

C) f(x) = x 4 + 26x 2 + 48

D) f(x) = x 4 + 13x 2 - 48

18) 7, -11, and 2 + 8i

A) f(x) = x 4 - 145x 2 + 580x - 5236

B) f(x) = x 4 - 25x 2 + 580x - 5236

C) f(x) = x 4 - 9x 3 - 56x 2 + 290x - 5236

D) f(x) = x 4 - 9x 3 + 56x 2 - 290x + 5236

Calin M. Agut - 2012

Zeros Of Polynomials Worksheet Template With Answer Key - Calin M. Agut Page 2

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