Find the Roots (Zeros) x(5x-2)(x^2+1)

$x (5 x - 2) (x^{2} + 1)$

Step 1

Set $x (5 x - 2) (x^{2} + 1)$ equal to $0$ .

$x (5 x - 2) (x^{2} + 1) = 0$

Step 2

Solve for $x$ .

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

$x = 0$

$5 x - 2 = 0$

$x^{2} + 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $5 x - 2$ equal to $0$ and solve for $x$ .

Set $5 x - 2$ equal to $0$ .

$5 x - 2 = 0$

Solve $5 x - 2 = 0$ for $x$ .

Add $2$ to both sides of the equation.

$5 x = 2$

Divide each term in $5 x = 2$ by $5$ and simplify.

Divide each term in $5 x = 2$ by $5$ .

$\frac{5 x}{5} = \frac{2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{2}{5}$

Divide $x$ by $1$ .

$x = \frac{2}{5}$

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

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

$x^{2} + 1 = 0$

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

Subtract $1$ from both sides of the equation.

$x^{2} = - 1$

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

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

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

$x = \pm i$

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.

$x = i$

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

$x = - i$

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

$x = i, - i$

The final solution is all the values that make $x (5 x - 2) (x^{2} + 1) = 0$ true.

$x = 0, \frac{2}{5}, i, - i$

Step 3

Find the Roots (Zeros) x(5x-2)(x^2+1)

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