Question

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

Answer 1

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