Solve 3x^2 - 13x^4

Question

Factor the expression

x^{2} (3 - 13 x^{2})

Evaluate

3 x^{2} - 13 x^{4}

Rewrite the expression

x^{2} \times 3 - x^{2} \times 13 x^{2}

Solution

x^{2} (3 - 13 x^{2})

Show Solution

x_{1} = - \frac{39}{13}, x_{2} = 0, x_{3} = \frac{39}{13}

Alternative Form

x_{1} \approx - 0.480384, x_{2} = 0, x_{3} \approx 0.480384

Evaluate

3 x^{2} - 13 x^{4}

To find the roots of the expression,set the expression equal to 0

3 x^{2} - 13 x^{4} = 0

Factor the expression

x^{2} (3 - 13 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 3 - 13 x^{2} = 0

The only way a power can be 0 is when the base equals 0

x = 0 3 - 13 x^{2} = 0

Solve the equation

More Steps

Evaluate

3 - 13 x^{2} = 0

Move the constant to the right-hand side and change its sign

- 13 x^{2} = 0 - 3

Removing 0 doesn't change the value,so remove it from the expression

- 13 x^{2} = - 3

Change the signs on both sides of the equation

13 x^{2} = 3

Divide both sides

\frac{13 x ^{2}}{13} = \frac{3}{13}

Divide the numbers

x^{2} = \frac{3}{13}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{3}{13}

Simplify the expression

More Steps

Evaluate

\frac{3}{13}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3}{13}

Multiply by the Conjugate

\frac{3 \times 13}{13 \times 13}

Multiply the numbers

\frac{39}{13 \times 13}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{39}{13}

x = \pm \frac{39}{13}

Separate the equation into 2 possible cases

x = \frac{39}{13} x = - \frac{39}{13}

x = 0 x = \frac{39}{13} x = - \frac{39}{13}

Solution

x_{1} = - \frac{39}{13}, x_{2} = 0, x_{3} = \frac{39}{13}

Alternative Form

x_{1} \approx - 0.480384, x_{2} = 0, x_{3} \approx 0.480384

Show Solution