What are the solutions to the equation x^4-2x^3+5x^2-8x+4=0 ?

The solutions to the equation x^4-2x^3+5x^2-8x+4=0 are x=1,x=2i,x=-2i

Find the zeros of x^4-2x^3+5x^2-8x+4=0

The zeros of x^4-2x^3+5x^2-8x+4=0 are x=1,x=2i,x=-2i

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x^{4} - 2 x^{3} + 5 x^{2} - 8 x + 4 = 0

x = 1, x = 2 i, x = - 2 i

Solution steps

x^{4} - 2 x^{3} + 5 x^{2} - 8 x + 4 = 0

Factor

x^{4} - 2 x^{3} + 5 x^{2} - 8 x + 4 : (x - 1)^{2} (x^{2} + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

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

The solutions are

x = 1, x = 2 i, x = - 2 i

\frac{x ^{3}}{7} - 21 x = 0

2 x^{4} - 3 x^{3} - 7 x^{2} - 8 x + 6 = 0

- 3 x^{3} + 4 x^{2} - 12 x + 16 = 0

a^{3} + 3 a^{2} + 2 a = 0

y^{4} - 3 y^{2} - 4 = 0

What are the solutions to the equation x^4-2x^3+5x^2-8x+4=0 ?
The solutions to the equation x^4-2x^3+5x^2-8x+4=0 are x=1,x=2i,x=-2i
Find the zeros of x^4-2x^3+5x^2-8x+4=0
The zeros of x^4-2x^3+5x^2-8x+4=0 are x=1,x=2i,x=-2i