Find the Roots (Zeros) x^3+x^2+x=0

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

Factor $x$ out of $x^{3} + x^{2} + x$ .

Factor $x$ out of $x^{3}$ .

$x \cdot x^{2} + x^{2} + x = 0$

Factor $x$ out of $x^{2}$ .

$x \cdot x^{2} + x \cdot x + x = 0$

Raise $x$ to the power of $1$ .

$x \cdot x^{2} + x \cdot x + x = 0$

Factor $x$ out of $x^{1}$ .

$x \cdot x^{2} + x \cdot x + x \cdot 1 = 0$

Factor $x$ out of $x \cdot x^{2} + x \cdot x$ .

$x (x^{2} + x) + x \cdot 1 = 0$

Factor $x$ out of $x (x^{2} + x) + x \cdot 1$ .

$x (x^{2} + x + 1) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x^{2} + x + 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x^{2} + x + 1$ equal to $0$ and solve for $x$ .

Set $x^{2} + x + 1$ equal to $0$ .

$x^{2} + x + 1 = 0$

Solve $x^{2} + x + 1 = 0$ for $x$ .

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = 1$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (1 \cdot 1)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot 1}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4}}{2 \cdot 1}$

Subtract $4$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 3}}{2 \cdot 1}$

Rewrite $- 3$ as $- 1 (3)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 3}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{3}}{2 \cdot 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 1 \pm i \sqrt{3}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 1 \pm i \sqrt{3}}{2}$

The final answer is the combination of both solutions.

$x = - \frac{1 - i \sqrt{3}}{2}, - \frac{1 + i \sqrt{3}}{2}$

The final solution is all the values that make $x (x^{2} + x + 1) = 0$ true.

$x = 0, - \frac{1 - i \sqrt{3}}{2}, - \frac{1 + i \sqrt{3}}{2}$

Find the Roots (Zeros) x^3+x^2+x=0

Related Questions

Support LCMGCF.com by disabling your adblocker.