Solve 3x^3-2x^5 - ScanMath

Question

Factor the expression

x^{3} (3 - 2 x^{2})

Evaluate

3 x^{3} - 2 x^{5}

Rewrite the expression

x^{3} \times 3 - x^{3} \times 2 x^{2}

Solution

x^{3} (3 - 2 x^{2})

Show Solution

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

Alternative Form

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

Evaluate

3 x^{3} - 2 x^{5}

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

3 x^{3} - 2 x^{5} = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

3 - 2 x^{2} = 0

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

- 2 x^{2} = 0 - 3

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

- 2 x^{2} = - 3

Change the signs on both sides of the equation

2 x^{2} = 3

Divide both sides

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

Divide the numbers

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

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

x = \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}

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

Separate the equation into 2 possible cases

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

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

Solution

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

Alternative Form

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

Show Solution