Find the Roots (Zeros) -x^3+5x^2-11x+55=0

$- x^{3} + 5 x^{2} - 11 x + 55 = 0$

Step 1

Factor the left side of the equation.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- x^{3} + 5 x^{2}) - 11 x + 55 = 0$

Factor out the greatest common factor (GCF) from each group.

$x^{2} (- x + 5) + 11 (- x + 5) = 0$

Factor the polynomial by factoring out the greatest common factor, $- x + 5$ .

$(- x + 5) (x^{2} + 11) = 0$

Step 2

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

$- x + 5 = 0$

$x^{2} + 11 = 0$

Step 3

Set $- x + 5$ equal to $0$ and solve for $x$ .

Set $- x + 5$ equal to $0$ .

$- x + 5 = 0$

Solve $- x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$- x = - 5$

Divide each term in $- x = - 5$ by $- 1$ and simplify.

Divide each term in $- x = - 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 5}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$x = 5$

Step 4

Set $x^{2} + 11$ equal to $0$ and solve for $x$ .

Set $x^{2} + 11$ equal to $0$ .

$x^{2} + 11 = 0$

Solve $x^{2} + 11 = 0$ for $x$ .

Subtract $11$ from both sides of the equation.

$x^{2} = - 11$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 11}$

Simplify $\pm \sqrt{- 11}$ .

Rewrite $- 11$ as $- 1 (11)$ .

$x = \pm \sqrt{- 1 (11)}$

Rewrite $\sqrt{- 1 (11)}$ as $\sqrt{- 1} \cdot \sqrt{11}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{11}$

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

$x = \pm i \sqrt{11}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = i \sqrt{11}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - i \sqrt{11}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = i \sqrt{11}, - i \sqrt{11}$

Step 5

The final solution is all the values that make $(- x + 5) (x^{2} + 11) = 0$ true.

$x = 5, i \sqrt{11}, - i \sqrt{11}$

Step 6

Find the Roots (Zeros) -x^3+5x^2-11x+55=0

Related Questions

Support LCMGCF.com by disabling your adblocker.