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Find all the roots of x^3 + 5x^2 + x + 5 = 0.Show step by step solution to explain the...

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Find all the roots of x^3 + 5x^2 + x + 5 = 0.

Show step by step solution to explain the answer.

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`x^3+5x^2+x+5=0`

We can find the factors as below.

`x^2(x+5)+1(x+5) = 0`

`(x^2+1)(x+5) =0`

Therefore the roots are, `x = -5` and `x^2+1 = 0`
, which gives, `x = +-i`

 

The roots are `{-i, +i, 5}`

 

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