Solve f^24-120f^4

Question

Simplify the expression

4 f^{2} - 120 f^{4}

Evaluate

f^{2} \times 4 - 120 f^{4}

Solution

4 f^{2} - 120 f^{4}

Show Solution

4 f^{2} (1 - 30 f^{2})

Evaluate

f^{2} \times 4 - 120 f^{4}

Use the commutative property to reorder the terms

4 f^{2} - 120 f^{4}

Rewrite the expression

4 f^{2} - 4 f^{2} \times 30 f^{2}

Solution

4 f^{2} (1 - 30 f^{2})

Show Solution

f_{1} = - \frac{30}{30}, f_{2} = 0, f_{3} = \frac{30}{30}

Alternative Form

f_{1} \approx - 0.182574, f_{2} = 0, f_{3} \approx 0.182574

Evaluate

f^{2} \times 4 - 120 f^{4}

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

f^{2} \times 4 - 120 f^{4} = 0

Use the commutative property to reorder the terms

4 f^{2} - 120 f^{4} = 0

Factor the expression

4 f^{2} (1 - 30 f^{2}) = 0

Divide both sides

f^{2} (1 - 30 f^{2}) = 0

Separate the equation into 2 possible cases

f^{2} = 0 1 - 30 f^{2} = 0

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

f = 0 1 - 30 f^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 30 f^{2} = 0

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

- 30 f^{2} = 0 - 1

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

- 30 f^{2} = - 1

Change the signs on both sides of the equation

30 f^{2} = 1

Divide both sides

\frac{30 f ^{2}}{30} = \frac{1}{30}

Divide the numbers

f^{2} = \frac{1}{30}

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

f = \pm \frac{1}{30}

Simplify the expression

More Steps

Evaluate

\frac{1}{30}

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

\frac{1}{30}

Simplify the radical expression

\frac{1}{30}

Multiply by the Conjugate

\frac{30}{30 \times 30}

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

\frac{30}{30}

f = \pm \frac{30}{30}

Separate the equation into 2 possible cases

f = \frac{30}{30} f = - \frac{30}{30}

f = 0 f = \frac{30}{30} f = - \frac{30}{30}

Solution

f_{1} = - \frac{30}{30}, f_{2} = 0, f_{3} = \frac{30}{30}

Alternative Form

f_{1} \approx - 0.182574, f_{2} = 0, f_{3} \approx 0.182574

Show Solution