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

Question

Simplify the expression

4 x^{6} - 3 x^{3}

Evaluate

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

Multiply

More Steps

Multiply the terms

x^{4} \times 4 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 4

Add the numbers

x^{6} \times 4

Use the commutative property to reorder the terms

4 x^{6}

4 x^{6} - 3 x^{3} \times 1

Solution

4 x^{6} - 3 x^{3}

Show Solution

Factor the expression

x^{3} (4 x^{3} - 3)

Evaluate

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

Multiply

More Steps

Multiply the terms

x^{4} \times 4 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 4

Add the numbers

x^{6} \times 4

Use the commutative property to reorder the terms

4 x^{6}

4 x^{6} - 3 x^{3} \times 1

Multiply the terms

4 x^{6} - 3 x^{3}

Rewrite the expression

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

Solution

x^{3} (4 x^{3} - 3)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 6}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 0.90856

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

x^{4} \times 4 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 4

Add the numbers

x^{6} \times 4

Use the commutative property to reorder the terms

4 x^{6}

4 x^{6} - 3 x^{3} \times 1 = 0

Multiply the terms

4 x^{6} - 3 x^{3} = 0

Factor the expression

x^{3} (4 x^{3} - 3) = 0

Separate the equation into 2 possible cases

x^{3} = 0 4 x^{3} - 3 = 0

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

x = 0 4 x^{3} - 3 = 0

Solve the equation

More Steps

Evaluate

4 x^{3} - 3 = 0

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

4 x^{3} = 0 + 3

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

4 x^{3} = 3

Divide both sides

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

Divide the numbers

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

Take the 3 -th root on both sides of the equation

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

Calculate

x = 3 \frac{3}{4}

Simplify the root

More Steps

Evaluate

3 \frac{3}{4}

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

\frac{3 3}{3 4}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

\frac{2 3 6}{3 4 \times 3 4 ^{2}}

Multiply the numbers

\frac{2 3 6}{2 ^{2}}

Reduce the fraction

\frac{3 6}{2}

x = \frac{3 6}{2}

x = 0 x = \frac{3 6}{2}

Solution

x_{1} = 0, x_{2} = \frac{3 6}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 0.90856

Show Solution