Lesson
Complex Zeros
Information is
g
iven about a pol
y
nomial f(x) whose coefficients are real numbers. Find the remainin
g
zeros of f.
1) Degree 3; zeros: 3, 1 - i
2) Degree 4; zeros: i, 2 + i
3) Degree 5; zeros: 6, 3 + 5i, -6i
4) Degree 6; zeros: 3, 2 + i, -4 - i, 0
Form a pol
y
nomial f(x) with real coefficients havin
g
the
g
iven de
g
ree and zeros.
5) Degree 3: zeros: 1 + i and -10
6) Degree: 3; zeros: -2 and 3 + i.
7) Degree: 4; zeros: -1, 2, and 1 - 2i.
Use the
g
iven zero to find the remainin
g
zeros of the function.
8) f(x) = x4 - 12x2 - 64; zero: -2i
9) f(x) = x3 - 2x2 - 11x + 52; zero: -4
10) f(x) = x3 + 5x2 + 17x + 13; zero: -2 + 3i
Find all zeros of the function and write the pol
y
nomial as a product of linear factors.
11) f(x) = x3 - x2 + 25x - 25
12) f(x) = x3 + 6x2 + 1x - 34
13) f(x) = x3 + 3x2 + 3x - 7
14) f(x) = x4 + 6x3 + 17x2 + 54x + 72
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