Solve 2400848 z^4-2

Question

Factor the expression

2 (1200424 z^{4} - 1)

Evaluate

2400848 z^{4} - 2

Solution

2 (1200424 z^{4} - 1)

Show Solution

z_{1} = - \frac{4 120042 4 ^{3}}{1200424}, z_{2} = \frac{4 120042 4 ^{3}}{1200424}

Alternative Form

z_{1} \approx - 0.030211, z_{2} \approx 0.030211

Evaluate

2400848 z^{4} - 2

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

2400848 z^{4} - 2 = 0

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

2400848 z^{4} = 0 + 2

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

2400848 z^{4} = 2

Divide both sides

\frac{2400848 z ^{4}}{2400848} = \frac{2}{2400848}

Divide the numbers

z^{4} = \frac{2}{2400848}

Cancel out the common factor 2

z^{4} = \frac{1}{1200424}

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

z = \pm 4 \frac{1}{1200424}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{1200424}

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

\frac{4 1}{4 1200424}

Simplify the radical expression

\frac{1}{4 1200424}

Multiply by the Conjugate

\frac{4 120042 4 ^{3}}{4 1200424 \times 4 120042 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

41200424 \times 4 120042 4^{3}

The product of roots with the same index is equal to the root of the product

4 1200424 \times 120042 4^{3}

Calculate the product

4 120042 4^{4}

Reduce the index of the radical and exponent with 4

1200424

\frac{4 120042 4 ^{3}}{1200424}

z = \pm \frac{4 120042 4 ^{3}}{1200424}

Separate the equation into 2 possible cases

z = \frac{4 120042 4 ^{3}}{1200424} z = - \frac{4 120042 4 ^{3}}{1200424}

Solution

z_{1} = - \frac{4 120042 4 ^{3}}{1200424}, z_{2} = \frac{4 120042 4 ^{3}}{1200424}

Alternative Form

z_{1} \approx - 0.030211, z_{2} \approx 0.030211

Show Solution