Solve 3k^2-2k^4=0

Question

Solve the equation

k_{1} = - \frac{6}{2}, k_{2} = 0, k_{3} = \frac{6}{2}

Alternative Form

k_{1} \approx - 1.224745, k_{2} = 0, k_{3} \approx 1.224745

Evaluate

3 k^{2} - 2 k^{4} = 0

Factor the expression

k^{2} (3 - 2 k^{2}) = 0

Separate the equation into 2 possible cases

k^{2} = 0 3 - 2 k^{2} = 0

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

k = 0 3 - 2 k^{2} = 0

Solve the equation

More Steps

Evaluate

3 - 2 k^{2} = 0

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

- 2 k^{2} = 0 - 3

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

- 2 k^{2} = - 3

Change the signs on both sides of the equation

2 k^{2} = 3

Divide both sides

\frac{2 k ^{2}}{2} = \frac{3}{2}

Divide the numbers

k^{2} = \frac{3}{2}

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

k = \pm \frac{3}{2}

Simplify the expression

More Steps

Evaluate

\frac{3}{2}

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

\frac{3}{2}

Multiply by the Conjugate

\frac{3 \times 2}{2 \times 2}

Multiply the numbers

\frac{6}{2 \times 2}

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

\frac{6}{2}

k = \pm \frac{6}{2}

Separate the equation into 2 possible cases

k = \frac{6}{2} k = - \frac{6}{2}

k = 0 k = \frac{6}{2} k = - \frac{6}{2}

Solution

k_{1} = - \frac{6}{2}, k_{2} = 0, k_{3} = \frac{6}{2}

Alternative Form

k_{1} \approx - 1.224745, k_{2} = 0, k_{3} \approx 1.224745

Show Solution