What are the solutions to the equation x^4-8x^3+24x^2-32x=0 ?

The solutions to the equation x^4-8x^3+24x^2-32x=0 are x=0,x=4,x=2+2i,x=2-2i

Find the zeros of x^4-8x^3+24x^2-32x=0

The zeros of x^4-8x^3+24x^2-32x=0 are x=0,x=4,x=2+2i,x=2-2i

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x^{4} - 8 x^{3} + 24 x^{2} - 32 x = 0

x = 0, x = 4, x = 2 + 2 i, x = 2 - 2 i

Solution steps

x^{4} - 8 x^{3} + 24 x^{2} - 32 x = 0

Factor

x^{4} - 8 x^{3} + 24 x^{2} - 32 x : x (x - 4) (x^{2} - 4 x + 8)

x (x - 4) (x^{2} - 4 x + 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 4 = 0 or x^{2} - 4 x + 8 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{2} - 4 x + 8 = 0 : x = 2 + 2 i, x = 2 - 2 i

The solutions are

x = 0, x = 4, x = 2 + 2 i, x = 2 - 2 i

x^{3} - 10 x + 21 = 0

x^{4} - 12 x^{2} + 16 = 0

2 (x^{2} - 2 x)^{2} - 5 (x^{2} - 2 x) = 6

27 x^{3} + 36 x = 8 + 54 x^{2}

729 = x^{3}

What are the solutions to the equation x^4-8x^3+24x^2-32x=0 ?
The solutions to the equation x^4-8x^3+24x^2-32x=0 are x=0,x=4,x=2+2i,x=2-2i
Find the zeros of x^4-8x^3+24x^2-32x=0
The zeros of x^4-8x^3+24x^2-32x=0 are x=0,x=4,x=2+2i,x=2-2i