Find the Roots (Zeros) y equals x to the power of three minus five x to the power of two plus nine x minus forty-five

$y = x^{3} - 5 x^{2} + 9 x - 45$

Set $x^{3} - 5 x^{2} + 9 x - 45$ equal to $0$ .

$x^{3} - 5 x^{2} + 9 x - 45 = 0$

Calculate $x$ .

Tap for more steps...

The left part of the equation should be factored.

Tap for more steps...

Take the greatest common factor from each group out of the brackets.

Tap for more steps...

Put together the Initially two terms and the last two terms.

$(x^{3} - 5 x^{2}) + 9 x - 45 = 0$

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

$x^{2} (x - 5) + 9 (x - 5) = 0$

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

$(x - 5) (x^{2} + 9) = 0$

In case any individual factor in the left part of the equation equals $0$ , the entire expression will be equal to $0$ .

$x - 5 = 0$

$x^{2} + 9 = 0$

Make the initial factor equal to $0$ and solve.

Tap for more steps...

Set the first factor equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Make the following factor equal to $0$ and solve.

Tap for more steps...

Set the Then factor equal to $0$ .

$x^{2} + 9 = 0$

Subtract $9$ from both sides of the equation.

$x^{2} = - 9$

To reduce the exponent on the left, square the roots of both sides of the equation.

$x = \pm \sqrt{- 9}$

The total solution is the sum of the solution's positive and negative components.

Tap for more steps...

Clarify the right side of the equation.

Tap for more steps...

Should be rewritten $- 9$ as $- 1 (9)$ .

$x = \pm \sqrt{- 1 \cdot 9}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{9}$

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

$x = \pm i \cdot \sqrt{9}$

Rewrite $9$ as $3^{2}$ .

$x = \pm i \cdot \sqrt{3^{2}}$

Withdraw terms from under the radical, assuming positive real numbers.

$x = \pm i \cdot 3$

Put $3$ to the left of $i$ .

$x = \pm 3 i$

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

Tap for more steps...

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

$x = 3 i$

Then, use the negative value of the $\pm$ To calculate the second answer.

$x = - 3 i$

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

$x = 3 i, - 3 i$

The final solution is all the values that make $(x - 5) (x^{2} + 9) = 0$ true.

$x = 5, 3 i, - 3 i$

Do you need help with solving Find the Roots (Zeros) y=x^3-5x^2+9x-45? We can help you. You can write to our math experts in our application. The best solution for you is above on this page.

Evaluate (minus six hundred twenty-five) to the power of(one First, divide four)

Find the Maximum First, divide Minimum Value P(x) equals minus six x to the power of two plus three hundred thirty-six x minus four thousand three hundred twenty

Find the Maximum First, divide Minimum Value f(x) equals three x to the power of two plus eighteen x plus twenty-five

Find the Inverse square root of eight plus x

Solve for x five x minus three y equals minus fifteen