Solve 4d^2-11d^6 - ScanMath

Question

Factor the expression

d^{2} (4 - 11 d^{4})

Evaluate

4 d^{2} - 11 d^{6}

Rewrite the expression

d^{2} \times 4 - d^{2} \times 11 d^{4}

Solution

d^{2} (4 - 11 d^{4})

Show Solution

d_{1} = - \frac{4 5324}{11}, d_{2} = 0, d_{3} = \frac{4 5324}{11}

Alternative Form

d_{1} \approx - 0.776545, d_{2} = 0, d_{3} \approx 0.776545

Evaluate

4 d^{2} - 11 d^{6}

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

4 d^{2} - 11 d^{6} = 0

Factor the expression

d^{2} (4 - 11 d^{4}) = 0

Separate the equation into 2 possible cases

d^{2} = 0 4 - 11 d^{4} = 0

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

d = 0 4 - 11 d^{4} = 0

Solve the equation

More Steps

Evaluate

4 - 11 d^{4} = 0

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

- 11 d^{4} = 0 - 4

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

- 11 d^{4} = - 4

Change the signs on both sides of the equation

11 d^{4} = 4

Divide both sides

\frac{11 d ^{4}}{11} = \frac{4}{11}

Divide the numbers

d^{4} = \frac{4}{11}

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

d = \pm 4 \frac{4}{11}

Simplify the expression

More Steps

Evaluate

4 \frac{4}{11}

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

\frac{4 4}{4 11}

Simplify the radical expression

\frac{2}{4 11}

Multiply by the Conjugate

\frac{2 \times 4 1 1 ^{3}}{4 11 \times 4 1 1 ^{3}}

Simplify

\frac{2 \times 4 1331}{4 11 \times 4 1 1 ^{3}}

Multiply the numbers

\frac{4 5324}{4 11 \times 4 1 1 ^{3}}

Multiply the numbers

\frac{4 5324}{11}

d = \pm \frac{4 5324}{11}

Separate the equation into 2 possible cases

d = \frac{4 5324}{11} d = - \frac{4 5324}{11}

d = 0 d = \frac{4 5324}{11} d = - \frac{4 5324}{11}

Solution

d_{1} = - \frac{4 5324}{11}, d_{2} = 0, d_{3} = \frac{4 5324}{11}

Alternative Form

d_{1} \approx - 0.776545, d_{2} = 0, d_{3} \approx 0.776545

Show Solution