Solve k^2-13k^48 - ScanMath

Question

Simplify the expression

k^{2} - 104 k^{4}

Evaluate

k^{2} - 13 k^{4} \times 8

Solution

k^{2} - 104 k^{4}

Show Solution

k^{2} (1 - 104 k^{2})

Evaluate

k^{2} - 13 k^{4} \times 8

Multiply the terms

k^{2} - 104 k^{4}

Rewrite the expression

k^{2} - k^{2} \times 104 k^{2}

Solution

k^{2} (1 - 104 k^{2})

Show Solution

k_{1} = - \frac{26}{52}, k_{2} = 0, k_{3} = \frac{26}{52}

Alternative Form

k_{1} \approx - 0.098058, k_{2} = 0, k_{3} \approx 0.098058

Evaluate

k^{2} - 13 k^{4} \times 8

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

k^{2} - 13 k^{4} \times 8 = 0

Multiply the terms

k^{2} - 104 k^{4} = 0

Factor the expression

k^{2} (1 - 104 k^{2}) = 0

Separate the equation into 2 possible cases

k^{2} = 0 1 - 104 k^{2} = 0

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

k = 0 1 - 104 k^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 104 k^{2} = 0

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

- 104 k^{2} = 0 - 1

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

- 104 k^{2} = - 1

Change the signs on both sides of the equation

104 k^{2} = 1

Divide both sides

\frac{104 k ^{2}}{104} = \frac{1}{104}

Divide the numbers

k^{2} = \frac{1}{104}

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

k = \pm \frac{1}{104}

Simplify the expression

More Steps

Evaluate

\frac{1}{104}

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

\frac{1}{104}

Simplify the radical expression

\frac{1}{104}

Simplify the radical expression

\frac{1}{2 26}

Multiply by the Conjugate

\frac{26}{2 26 \times 26}

Multiply the numbers

\frac{26}{52}

k = \pm \frac{26}{52}

Separate the equation into 2 possible cases

k = \frac{26}{52} k = - \frac{26}{52}

k = 0 k = \frac{26}{52} k = - \frac{26}{52}

Solution

k_{1} = - \frac{26}{52}, k_{2} = 0, k_{3} = \frac{26}{52}

Alternative Form

k_{1} \approx - 0.098058, k_{2} = 0, k_{3} \approx 0.098058

Show Solution