Solve 3a^2 - 8a^4

Question

Factor the expression

a^{2} (3 - 8 a^{2})

Evaluate

3 a^{2} - 8 a^{4}

Rewrite the expression

a^{2} \times 3 - a^{2} \times 8 a^{2}

Solution

a^{2} (3 - 8 a^{2})

Show Solution

a_{1} = - \frac{6}{4}, a_{2} = 0, a_{3} = \frac{6}{4}

Alternative Form

a_{1} \approx - 0.612372, a_{2} = 0, a_{3} \approx 0.612372

Evaluate

3 a^{2} - 8 a^{4}

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

3 a^{2} - 8 a^{4} = 0

Factor the expression

a^{2} (3 - 8 a^{2}) = 0

Separate the equation into 2 possible cases

a^{2} = 0 3 - 8 a^{2} = 0

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

a = 0 3 - 8 a^{2} = 0

Solve the equation

More Steps

Evaluate

3 - 8 a^{2} = 0

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

- 8 a^{2} = 0 - 3

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

- 8 a^{2} = - 3

Change the signs on both sides of the equation

8 a^{2} = 3

Divide both sides

\frac{8 a ^{2}}{8} = \frac{3}{8}

Divide the numbers

a^{2} = \frac{3}{8}

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

a = \pm \frac{3}{8}

Simplify the expression

More Steps

Evaluate

\frac{3}{8}

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

\frac{3}{8}

Simplify the radical expression

\frac{3}{2 2}

Multiply by the Conjugate

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

Multiply the numbers

\frac{6}{2 2 \times 2}

Multiply the numbers

\frac{6}{4}

a = \pm \frac{6}{4}

Separate the equation into 2 possible cases

a = \frac{6}{4} a = - \frac{6}{4}

a = 0 a = \frac{6}{4} a = - \frac{6}{4}

Solution

a_{1} = - \frac{6}{4}, a_{2} = 0, a_{3} = \frac{6}{4}

Alternative Form

a_{1} \approx - 0.612372, a_{2} = 0, a_{3} \approx 0.612372

Show Solution