Solve 9u^2-12u^4 - ScanMath

Question

Factor the expression

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

Evaluate

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

Rewrite the expression

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

Solution

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

Show Solution

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

Alternative Form

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

Evaluate

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

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

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

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

3 - 4 u^{2} = 0

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

- 4 u^{2} = 0 - 3

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

- 4 u^{2} = - 3

Change the signs on both sides of the equation

4 u^{2} = 3

Divide both sides

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

Divide the numbers

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

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

u = \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}

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

Separate the equation into 2 possible cases

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

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

Solution

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

Alternative Form

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

Show Solution