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

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


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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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