Solve 9y^2 -12y^4

Question

Factor the expression

3 y^{2} (3 - 4 y^{2})

Evaluate

9 y^{2} - 12 y^{4}

Rewrite the expression

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

Solution

3 y^{2} (3 - 4 y^{2})

Show Solution

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

Alternative Form

y_{1} \approx - 0.866025, y_{2} = 0, y_{3} \approx 0.866025

Evaluate

9 y^{2} - 12 y^{4}

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

9 y^{2} - 12 y^{4} = 0

Factor the expression

3 y^{2} (3 - 4 y^{2}) = 0

Divide both sides

y^{2} (3 - 4 y^{2}) = 0

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

3 - 4 y^{2} = 0

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

- 4 y^{2} = 0 - 3

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

- 4 y^{2} = - 3

Change the signs on both sides of the equation

4 y^{2} = 3

Divide both sides

\frac{4 y ^{2}}{4} = \frac{3}{4}

Divide the numbers

y^{2} = \frac{3}{4}

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

y = \pm \frac{3}{4}

Simplify the expression

More Steps

Evaluate

\frac{3}{4}

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

\frac{3}{4}

Simplify the radical expression

\frac{3}{2}

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

Separate the equation into 2 possible cases

y = \frac{3}{2} y = - \frac{3}{2}

y = 0 y = \frac{3}{2} y = - \frac{3}{2}

Solution

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

Alternative Form

y_{1} \approx - 0.866025, y_{2} = 0, y_{3} \approx 0.866025

Show Solution