Solve 5x^2-3x^4 - ScanMath

Question

Factor the expression

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

Evaluate

5 x^{2} - 3 x^{4}

Rewrite the expression

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

Solution

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

Show Solution

x_{1} = - \frac{15}{3}, x_{2} = 0, x_{3} = \frac{15}{3}

Alternative Form

x_{1} \approx - 1.290994, x_{2} = 0, x_{3} \approx 1.290994

Evaluate

5 x^{2} - 3 x^{4}

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

5 x^{2} - 3 x^{4} = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

5 - 3 x^{2} = 0

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

- 3 x^{2} = 0 - 5

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

- 3 x^{2} = - 5

Change the signs on both sides of the equation

3 x^{2} = 5

Divide both sides

\frac{3 x ^{2}}{3} = \frac{5}{3}

Divide the numbers

x^{2} = \frac{5}{3}

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

x = \pm \frac{5}{3}

Simplify the expression

More Steps

Evaluate

\frac{5}{3}

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

\frac{5}{3}

Multiply by the Conjugate

\frac{5 \times 3}{3 \times 3}

Multiply the numbers

\frac{15}{3 \times 3}

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

\frac{15}{3}

x = \pm \frac{15}{3}

Separate the equation into 2 possible cases

x = \frac{15}{3} x = - \frac{15}{3}

x = 0 x = \frac{15}{3} x = - \frac{15}{3}

Solution

x_{1} = - \frac{15}{3}, x_{2} = 0, x_{3} = \frac{15}{3}

Alternative Form

x_{1} \approx - 1.290994, x_{2} = 0, x_{3} \approx 1.290994

Show Solution