if x=-1-3i is a root of f(x)=x^3+4x^2+14x+20, find all the other roots ( real and imaginary)?

Answers

Answer #1 | 06/02 2014 19:47

f(x) = x³ + 4x² + 14x + 20
f(x) = (x + 2)(x² + 2x + 10)
If the product of two factors equals zero,
then one or both factors equal zero.
If x + 2 = 0,
x = - 2
If x² + 2x + 10 = 0,
x² + 2x = - 10
x² + 2x + 1 = 1 - 10
(x + 1)² = - 9
x + 1 = √(- 9)
x + 1 = √9 √(- 1)
x + 1 = ± 3 i
x = - 1 ± 3 i
Other Root = - 1 + 3 i
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Answer #1| 06/02 2014 19:4762 %