What are the solutions to the equation 3x^4-3x^3-1x^2=0 ?

The solutions to the equation 3x^4-3x^3-1x^2=0 are x=0,x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6

Find the zeros of 3x^4-3x^3-1x^2=0

The zeros of 3x^4-3x^3-1x^2=0 are x=0,x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6

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

x = 0, x = \frac{3 + 21}{6}, x = \frac{3 - 21}{6}

Solution steps

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

Factor

3 x^{4} - 3 x^{3} - 1 \cdot x^{2} : x^{2} (3 x^{2} - 3 x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x^{2} - 3 x - 1 = 0

Solve

3 x^{2} - 3 x - 1 = 0 : x = \frac{3 + 21}{6}, x = \frac{3 - 21}{6}

The solutions are

x = 0, x = \frac{3 + 21}{6}, x = \frac{3 - 21}{6}

z \cdot z^{3} + 15 = 16.66

z^{3} - z^{2} + 4 z - 4 = 0

x^{4} - (4 \cdot x) + 5 = 0

y^{5} + y^{3} + y = 3

- 3 = x^{6} - 8

What are the solutions to the equation 3x^4-3x^3-1x^2=0 ?
The solutions to the equation 3x^4-3x^3-1x^2=0 are x=0,x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6
Find the zeros of 3x^4-3x^3-1x^2=0
The zeros of 3x^4-3x^3-1x^2=0 are x=0,x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6