Solve n^2 - 5n^4 - ScanMath

Question

Factor the expression

n^{2} (1 - 5 n^{2})

Evaluate

n^{2} - 5 n^{4}

Rewrite the expression

n^{2} - n^{2} \times 5 n^{2}

Solution

n^{2} (1 - 5 n^{2})

Show Solution

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

Alternative Form

n_{1} \approx - 0.447214, n_{2} = 0, n_{3} \approx 0.447214

Evaluate

n^{2} - 5 n^{4}

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

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

Factor the expression

n^{2} (1 - 5 n^{2}) = 0

Separate the equation into 2 possible cases

n^{2} = 0 1 - 5 n^{2} = 0

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

n = 0 1 - 5 n^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 5 n^{2} = 0

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

- 5 n^{2} = 0 - 1

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

- 5 n^{2} = - 1

Change the signs on both sides of the equation

5 n^{2} = 1

Divide both sides

\frac{5 n ^{2}}{5} = \frac{1}{5}

Divide the numbers

n^{2} = \frac{1}{5}

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

n = \pm \frac{1}{5}

Simplify the expression

More Steps

Evaluate

\frac{1}{5}

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

\frac{1}{5}

Simplify the radical expression

\frac{1}{5}

Multiply by the Conjugate

\frac{5}{5 \times 5}

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

\frac{5}{5}

n = \pm \frac{5}{5}

Separate the equation into 2 possible cases

n = \frac{5}{5} n = - \frac{5}{5}

n = 0 n = \frac{5}{5} n = - \frac{5}{5}

Solution

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

Alternative Form

n_{1} \approx - 0.447214, n_{2} = 0, n_{3} \approx 0.447214

Show Solution