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

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

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

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

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

x = 0, x = 4, x = i, x = - i

Solution steps

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

Factor

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

- x^{2} (x - 4) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 4 = 0 or x^{2} + 1 = 0

Solve

x - 4 = 0 : x = 4

Solve

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

The solutions are

x = 0, x = 4, x = i, x = - i

x^{4} + 2 x^{2} = 8

x^{3} - 11 x^{2} + 30 x = 0

x^{6} + 4 x^{3} + 16 = 0

(x - 7) (x^{2} - 36) = 0

x^{3} - x^{2} - 22 x + 40 = 0

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