Solve 4c^(2)-12c^(4)

Question

Factor the expression

4 c^{2} (1 - 3 c^{2})

Evaluate

4 c^{2} - 12 c^{4}

Rewrite the expression

4 c^{2} - 4 c^{2} \times 3 c^{2}

Solution

4 c^{2} (1 - 3 c^{2})

Show Solution

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

Alternative Form

c_{1} \approx - 0.57735, c_{2} = 0, c_{3} \approx 0.57735

Evaluate

4 c^{2} - 12 c^{4}

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

4 c^{2} - 12 c^{4} = 0

Factor the expression

4 c^{2} (1 - 3 c^{2}) = 0

Divide both sides

c^{2} (1 - 3 c^{2}) = 0

Separate the equation into 2 possible cases

c^{2} = 0 1 - 3 c^{2} = 0

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

c = 0 1 - 3 c^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 3 c^{2} = 0

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

- 3 c^{2} = 0 - 1

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

- 3 c^{2} = - 1

Change the signs on both sides of the equation

3 c^{2} = 1

Divide both sides

\frac{3 c ^{2}}{3} = \frac{1}{3}

Divide the numbers

c^{2} = \frac{1}{3}

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

c = \pm \frac{1}{3}

Simplify the expression

More Steps

Evaluate

\frac{1}{3}

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

\frac{1}{3}

Simplify the radical expression

\frac{1}{3}

Multiply by the Conjugate

\frac{3}{3 \times 3}

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

\frac{3}{3}

c = \pm \frac{3}{3}

Separate the equation into 2 possible cases

c = \frac{3}{3} c = - \frac{3}{3}

c = 0 c = \frac{3}{3} c = - \frac{3}{3}

Solution

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

Alternative Form

c_{1} \approx - 0.57735, c_{2} = 0, c_{3} \approx 0.57735

Show Solution