Solve 4n^2-17n^4 - Socratic AI (ScanMath)

Question

Factor the expression

n^{2} (4 - 17 n^{2})

Evaluate

4 n^{2} - 17 n^{4}

Rewrite the expression

n^{2} \times 4 - n^{2} \times 17 n^{2}

Solution

n^{2} (4 - 17 n^{2})

Show Solution

n_{1} = - \frac{2 17}{17}, n_{2} = 0, n_{3} = \frac{2 17}{17}

Alternative Form

n_{1} \approx - 0.485071, n_{2} = 0, n_{3} \approx 0.485071

Evaluate

4 n^{2} - 17 n^{4}

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

4 n^{2} - 17 n^{4} = 0

Factor the expression

n^{2} (4 - 17 n^{2}) = 0

Separate the equation into 2 possible cases

n^{2} = 0 4 - 17 n^{2} = 0

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

n = 0 4 - 17 n^{2} = 0

Solve the equation

More Steps

Evaluate

4 - 17 n^{2} = 0

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

- 17 n^{2} = 0 - 4

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

- 17 n^{2} = - 4

Change the signs on both sides of the equation

17 n^{2} = 4

Divide both sides

\frac{17 n ^{2}}{17} = \frac{4}{17}

Divide the numbers

n^{2} = \frac{4}{17}

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

n = \pm \frac{4}{17}

Simplify the expression

More Steps

Evaluate

\frac{4}{17}

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

\frac{4}{17}

Simplify the radical expression

\frac{2}{17}

Multiply by the Conjugate

\frac{2 17}{17 \times 17}

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

\frac{2 17}{17}

n = \pm \frac{2 17}{17}

Separate the equation into 2 possible cases

n = \frac{2 17}{17} n = - \frac{2 17}{17}

n = 0 n = \frac{2 17}{17} n = - \frac{2 17}{17}

Solution

n_{1} = - \frac{2 17}{17}, n_{2} = 0, n_{3} = \frac{2 17}{17}

Alternative Form

n_{1} \approx - 0.485071, n_{2} = 0, n_{3} \approx 0.485071

Show Solution