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

The solutions to the equation x^5-x^4-3x^3=0 are x=0,x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2

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

The zeros of x^5-x^4-3x^3=0 are x=0,x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2

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

x = 0, x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{2} - x - 3 = 0 : x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

The solutions are

x = 0, x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

x^{4} (x^{3} - 9) = - 8 x

6 + x^{3} = 222

(x - 4)^{2} = (x - 4)^{4}

2 x^{3} + 5 x - 1 = 0

x^{3} - x - 20 = 0

What are the solutions to the equation x^5-x^4-3x^3=0 ?
The solutions to the equation x^5-x^4-3x^3=0 are x=0,x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2
Find the zeros of x^5-x^4-3x^3=0
The zeros of x^5-x^4-3x^3=0 are x=0,x=(1+sqrt(13))/2 ,x=(1-sqrt(13))/2