Trigonometry Examples

$f (x) = (x - 1) (x - \sqrt{7 i}) (x + \sqrt{7 i})$

Step 1

Set $(x - 1) (x - \sqrt{7 i}) (x + \sqrt{7 i})$ equal to $0$ .

$(x - 1) (x - \sqrt{7 i}) (x + \sqrt{7 i}) = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

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

$x - 1 = 0$

$x - \sqrt{7 i} = 0$

$x + \sqrt{7 i} = 0$

Step 2.2

Set $x - 1$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.2.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 2.2.2

Add $1$ to both sides of the equation.

$x = 1$

Step 2.3

Set $x - \sqrt{7 i}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.3.1

Set $x - \sqrt{7 i}$ equal to $0$ .

$x - \sqrt{7 i} = 0$

Step 2.3.2

Add $\sqrt{7 i}$ to both sides of the equation.

$x = \sqrt{7 i}$

Step 2.4

Set $x + \sqrt{7 i}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.4.1

Set $x + \sqrt{7 i}$ equal to $0$ .

$x + \sqrt{7 i} = 0$

Step 2.4.2

Subtract $\sqrt{7 i}$ from both sides of the equation.

$x = - \sqrt{7 i}$

Step 2.5

The final solution is all the values that make $(x - 1) (x - \sqrt{7 i}) (x + \sqrt{7 i}) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 1$ (Multiplicity of $1$ )

$x = \sqrt{7 i}$ (Multiplicity of $1$ )

$x = - \sqrt{7 i}$ (Multiplicity of $1$ )

$x = 1$ (Multiplicity of $1$ )

$x = \sqrt{7 i}$ (Multiplicity of $1$ )

$x = - \sqrt{7 i}$ (Multiplicity of $1$ )

Step 3