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# Enter the number of complex zeros for the polynomial function in the box

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Enter the number of complex zeros for the polynomial function in the box

f(x) = x^5 + 4x^3 - 5x

Oct 27, 2017

### 1+0 Answers

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Solve for x:
x^5 + 4 x^3 - 5 x = 0

The left hand side factors into a product with four terms:
x (x - 1) (x + 1) (x^2 + 5) = 0

Split into four equations:
x - 1 = 0 or x = 0 or x + 1 = 0 or x^2 + 5 = 0

Add 1 to both sides:
x = 1 or x = 0 or x + 1 = 0 or x^2 + 5 = 0

Subtract 1 from both sides:
x = 1 or x = 0 or x = -1 or x^2 + 5 = 0

Subtract 5 from both sides:
x = 1 or x = 0 or x = -1 or x^2 = -5

Take the square root of both sides:
x = 1    or    x = 0    or    x = -1    or    x = i sqrt(5)    or    x = -i sqrt(5)

Oct 27, 2017