How do you find all the real and complex roots of $x^{3} + 4 x^{2} + 3 x = 0$ $x^3 + 4x^2 + 3x = 0$ ?

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How do you find all the real and complex roots of $x^{3} + 4 x^{2} + 3 x = 0$ $x^3 + 4x^2 + 3x = 0$ ?

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Answer 1 · 2018-03-20T09:54:50

$x^{3} + 4 x^{2} + 4 x = 0$ $x^3+4x^2+4x=0$
$x (x^{2} + 4 x + 3) = 0$ $x(x^2+4x+3)=0$
implies x=0 and $x^{2} + 4 x + 3 = 0$ $x^2 + 4x+3=0$
thus we got one root and the other two roots are obtained by solving $x^{2} + 4 x + 3 = 0$ $x^2 + 4x+3=0$
$(x + 1) (x + 3) = 0$ $(x+1)(x+3)=0$
implies x=-1,x=-3
hence the roots are x=0,-1,-3

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How do you find all the real and complex roots of $x^{3} + 4 x^{2} + 3 x = 0$ $x^3 + 4x^2 + 3x = 0$ ?

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