What are the solutions to the equation x^5-6x^4+10x^3-6x^2+9x=0 ?

The solutions to the equation x^5-6x^4+10x^3-6x^2+9x=0 are x=0,x=3,x=i,x=-i

Find the zeros of x^5-6x^4+10x^3-6x^2+9x=0

The zeros of x^5-6x^4+10x^3-6x^2+9x=0 are x=0,x=3,x=i,x=-i

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x^{5} - 6 x^{4} + 10 x^{3} - 6 x^{2} + 9 x = 0

x = 0, x = 3, x = i, x = - i

Solution steps

x^{5} - 6 x^{4} + 10 x^{3} - 6 x^{2} + 9 x = 0

Factor

x^{5} - 6 x^{4} + 10 x^{3} - 6 x^{2} + 9 x : x (x - 3)^{2} (x^{2} + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 1 = 0 : x = i, x = - i

The solutions are

x = 0, x = 3, x = i, x = - i

2 x^{3} + 7 x^{2} - 2 x - 7 = 0

4 x^{3} - 6 x^{2} - 1 = 0

x^{3} + x^{2} - 6 = 0

2 x^{4} - x^{3} - 3 x - 18 = 0

x^{13} + x + 90 = 0

What are the solutions to the equation x^5-6x^4+10x^3-6x^2+9x=0 ?
The solutions to the equation x^5-6x^4+10x^3-6x^2+9x=0 are x=0,x=3,x=i,x=-i
Find the zeros of x^5-6x^4+10x^3-6x^2+9x=0
The zeros of x^5-6x^4+10x^3-6x^2+9x=0 are x=0,x=3,x=i,x=-i