# How do you find all the real and complex roots of 2x^3 + 12x^2 + 50x = 0?

Mar 21, 2018

$x = 0 , - 3 - 4 i \text{ or } - 3 + 4 i$

#### Explanation:

$2 {x}^{3} + 12 {x}^{2} + 50 x = 0$

$\Leftrightarrow {x}^{3} + 6 {x}^{2} + 25 x = 0$

or $x \left({x}^{2} + 6 x + 25\right) = 0$

or $x \left(\left({x}^{2} + 6 x + 9\right) + 16\right) = 0$

or $x \left({\left(x + 3\right)}^{2} + {4}^{2}\right) = 0$

or $x \left({\left(x + 3\right)}^{2} - \left(- {4}^{2}\right)\right) = 0$

or $x \left({\left(x + 3\right)}^{2} - {\left(4 i\right)}^{2}\right) = 0$

or $x \left(x + 3 + 4 i\right) \left(x + 3 - 4 i\right) = 0$

Hence roots are $x = 0 , - 3 - 4 i \text{ or } - 3 + 4 i$