Solve 5v^2 -4v^4 - ScanMath

Question

Factor the expression

v^{2} (5 - 4 v^{2})

Evaluate

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

Rewrite the expression

v^{2} \times 5 - v^{2} \times 4 v^{2}

Solution

v^{2} (5 - 4 v^{2})

Show Solution

v_{1} = - \frac{5}{2}, v_{2} = 0, v_{3} = \frac{5}{2}

Alternative Form

v_{1} \approx - 1.118034, v_{2} = 0, v_{3} \approx 1.118034

Evaluate

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

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

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

Factor the expression

v^{2} (5 - 4 v^{2}) = 0

Separate the equation into 2 possible cases

v^{2} = 0 5 - 4 v^{2} = 0

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

v = 0 5 - 4 v^{2} = 0

Solve the equation

More Steps

Evaluate

5 - 4 v^{2} = 0

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

- 4 v^{2} = 0 - 5

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

- 4 v^{2} = - 5

Change the signs on both sides of the equation

4 v^{2} = 5

Divide both sides

\frac{4 v ^{2}}{4} = \frac{5}{4}

Divide the numbers

v^{2} = \frac{5}{4}

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

v = \pm \frac{5}{4}

Simplify the expression

More Steps

Evaluate

\frac{5}{4}

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

\frac{5}{4}

Simplify the radical expression

\frac{5}{2}

v = \pm \frac{5}{2}

Separate the equation into 2 possible cases

v = \frac{5}{2} v = - \frac{5}{2}

v = 0 v = \frac{5}{2} v = - \frac{5}{2}

Solution

v_{1} = - \frac{5}{2}, v_{2} = 0, v_{3} = \frac{5}{2}

Alternative Form

v_{1} \approx - 1.118034, v_{2} = 0, v_{3} \approx 1.118034

Show Solution