Solve v^2-2v^4 - ScanMath

Question

Factor the expression

v^{2} (1 - 2 v^{2})

Evaluate

v^{2} - 2 v^{4}

Rewrite the expression

v^{2} - v^{2} \times 2 v^{2}

Solution

v^{2} (1 - 2 v^{2})

Show Solution

v_{1} = - \frac{2}{2}, v_{2} = 0, v_{3} = \frac{2}{2}

Alternative Form

v_{1} \approx - 0.707107, v_{2} = 0, v_{3} \approx 0.707107

Evaluate

v^{2} - 2 v^{4}

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

v^{2} - 2 v^{4} = 0

Factor the expression

v^{2} (1 - 2 v^{2}) = 0

Separate the equation into 2 possible cases

v^{2} = 0 1 - 2 v^{2} = 0

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

v = 0 1 - 2 v^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 2 v^{2} = 0

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

- 2 v^{2} = 0 - 1

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

- 2 v^{2} = - 1

Change the signs on both sides of the equation

2 v^{2} = 1

Divide both sides

\frac{2 v ^{2}}{2} = \frac{1}{2}

Divide the numbers

v^{2} = \frac{1}{2}

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

v = \pm \frac{1}{2}

Simplify the expression

More Steps

Evaluate

\frac{1}{2}

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

\frac{1}{2}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

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

\frac{2}{2}

v = \pm \frac{2}{2}

Separate the equation into 2 possible cases

v = \frac{2}{2} v = - \frac{2}{2}

v = 0 v = \frac{2}{2} v = - \frac{2}{2}

Solution

v_{1} = - \frac{2}{2}, v_{2} = 0, v_{3} = \frac{2}{2}

Alternative Form

v_{1} \approx - 0.707107, v_{2} = 0, v_{3} \approx 0.707107

Show Solution