Solve d^43-d^2 - ScanMath

Question

Simplify the expression

3 d^{4} - d^{2}

Evaluate

d^{4} \times 3 - d^{2}

Solution

3 d^{4} - d^{2}

Show Solution

d^{2} (3 d^{2} - 1)

Evaluate

d^{4} \times 3 - d^{2}

Use the commutative property to reorder the terms

3 d^{4} - d^{2}

Rewrite the expression

d^{2} \times 3 d^{2} - d^{2}

Solution

d^{2} (3 d^{2} - 1)

Show Solution

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

Alternative Form

d_{1} \approx - 0.57735, d_{2} = 0, d_{3} \approx 0.57735

Evaluate

d^{4} \times 3 - d^{2}

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

d^{4} \times 3 - d^{2} = 0

Use the commutative property to reorder the terms

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

Factor the expression

d^{2} (3 d^{2} - 1) = 0

Separate the equation into 2 possible cases

d^{2} = 0 3 d^{2} - 1 = 0

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

d = 0 3 d^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

3 d^{2} - 1 = 0

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

3 d^{2} = 0 + 1

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

3 d^{2} = 1

Divide both sides

\frac{3 d ^{2}}{3} = \frac{1}{3}

Divide the numbers

d^{2} = \frac{1}{3}

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

d = \pm \frac{1}{3}

Simplify the expression

More Steps

Evaluate

\frac{1}{3}

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

\frac{1}{3}

Simplify the radical expression

\frac{1}{3}

Multiply by the Conjugate

\frac{3}{3 \times 3}

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

\frac{3}{3}

d = \pm \frac{3}{3}

Separate the equation into 2 possible cases

d = \frac{3}{3} d = - \frac{3}{3}

d = 0 d = \frac{3}{3} d = - \frac{3}{3}

Solution

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

Alternative Form

d_{1} \approx - 0.57735, d_{2} = 0, d_{3} \approx 0.57735

Show Solution