# Finding Root for Equations Worksheet

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Mathematics
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1. Determine how many, what type, and find the roots for f(x) = x
4
+ 21x
2
− 100.
How many- 4
What type- 2 real and 2 complex
Roots- -2, 2, -5i, 5i
x^4+21x^2-100
(x^2+25)(x^2-4)
[x^2-(-25)]
(x+5i), (x-5i), (x+2), (x-2)
2. Determine how many, what type, and find the roots for f(x) = x
3
− 5x
2
− 25x + 125.
How many- 3
What type- 2 real root
Roots- 5, 5, -5
x^3-5x^2-25x+125
(x^3-5x^2), (-25x+125)
x^2(x-5), -25(x-5)
(x^2-25)
(x+5)(x-5)^2
3. The following graph shows a seventh-degree polynomial:
Part 1: List the polynomial’s zeroes with possible multiplicities.
Zero- -5 multiplicity of 2, -1 multiplicity of 1, 4 multiplicity of 3, 7 multiplicity of 1
Part 2: Write a possible factored form of the seventh degree function.

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1. Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100. How many- 4 What type- 2 real and 2 complex Roots- -2, 2, -5i, 5i x^4+21x^2-100 (x^2+25)(x^2-4) [x^2-(-25)] (x+5i), (x-5i), (x+2), (x-2) 2. Determine how many, what type, and find the roots for f(x) = x3 − 5x2 − 25x + 125. How many- 3 What type- 2 real root Roots- 5, 5, -5 x^3-5x^2-25x+125 (x^3-5x^2), (-25x+125) x^2(x-5), -25(x-5) (x^2-25) (x+5)(x-5)^2 3. The following graph shows a seventh-degree polynomial: Part 1: List the polynomial’s zeroes with possible multiplicities. Zero- -5 multiplicity of 2, - ...
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