Solve x^(4)-2x^(3) 2x-1

Question

Simplify the expression

- 3 x^{4} - 1

Show Solution

x_{1} = - \frac{4 108}{6} + \frac{4 108}{6} i, x_{2} = \frac{4 108}{6} - \frac{4 108}{6} i

Alternative Form

x_{1} \approx - 0.537285 + 0.537285 i, x_{2} \approx 0.537285 - 0.537285 i

Evaluate

x^{4} - 2 x^{3} \times 2 x - 1

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

x^{4} - 2 x^{3} \times 2 x - 1 = 0

Multiply

More Steps

x^{4} - 4 x^{4} - 1 = 0

Subtract the terms

More Steps

- 3 x^{4} - 1 = 0

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

- 3 x^{4} = 0 + 1

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

- 3 x^{4} = 1

Change the signs on both sides of the equation

3 x^{4} = - 1

Divide both sides

\frac{3 x ^{4}}{3} = \frac{- 1}{3}

Divide the numbers

x^{4} = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{4} = - \frac{1}{3}

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

x = \pm 4 - \frac{1}{3}

Simplify the expression

More Steps

x = \pm (\frac{4 108}{6} - \frac{4 108}{6} i)

Separate the equation into 2 possible cases

x = \frac{4 108}{6} - \frac{4 108}{6} i x = - \frac{4 108}{6} + \frac{4 108}{6} i

Solution

x_{1} = - \frac{4 108}{6} + \frac{4 108}{6} i, x_{2} = \frac{4 108}{6} - \frac{4 108}{6} i

Alternative Form

x_{1} \approx - 0.537285 + 0.537285 i, x_{2} \approx 0.537285 - 0.537285 i

Show Solution