What are the solutions to the equation x^5-3x^4-3x^3=0 ?

The solutions to the equation x^5-3x^4-3x^3=0 are x=0,x=(3+sqrt(21))/2 ,x=(3-sqrt(21))/2

Find the zeros of x^5-3x^4-3x^3=0

The zeros of x^5-3x^4-3x^3=0 are x=0,x=(3+sqrt(21))/2 ,x=(3-sqrt(21))/2

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x^{5} - 3 x^{4} - 3 x^{3} = 0

x = 0, x = \frac{3 + 21}{2}, x = \frac{3 - 21}{2}

Decimal Notation

x = 0, x = 3.79128 \dots, x = - 0.79128 \dots

Solution steps

x^{5} - 3 x^{4} - 3 x^{3} = 0

Factor

x^{5} - 3 x^{4} - 3 x^{3} : x^{3} (x^{2} - 3 x - 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

x = 0, x = \frac{3 + 21}{2}, x = \frac{3 - 21}{2}

r^{5} + 5 r^{4} - 1 = 0

(a - 2) (a + 2) - (a - 2)^{2} a = 1

(x^{2} - 3 x + 3) (x^{2} - 2 x + 3) = 2 x^{2}

r^{3} = \frac{243}{72}

y^{3} = y + 24

What are the solutions to the equation x^5-3x^4-3x^3=0 ?
The solutions to the equation x^5-3x^4-3x^3=0 are x=0,x=(3+sqrt(21))/2 ,x=(3-sqrt(21))/2
Find the zeros of x^5-3x^4-3x^3=0
The zeros of x^5-3x^4-3x^3=0 are x=0,x=(3+sqrt(21))/2 ,x=(3-sqrt(21))/2