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

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Abhi Share
Mar 20, 2018

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

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