What are the solutions to the equation x^4-6x^3+11x^2-8x+2=0 ?

The solutions to the equation x^4-6x^3+11x^2-8x+2=0 are x=1,x=2+sqrt(2),x=2-sqrt(2)

Find the zeros of x^4-6x^3+11x^2-8x+2=0

The zeros of x^4-6x^3+11x^2-8x+2=0 are x=1,x=2+sqrt(2),x=2-sqrt(2)

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x^{4} - 6 x^{3} + 11 x^{2} - 8 x + 2 = 0

x = 1, x = 2 + 2, x = 2 - 2

Solution steps

x^{4} - 6 x^{3} + 11 x^{2} - 8 x + 2 = 0

Factor

x^{4} - 6 x^{3} + 11 x^{2} - 8 x + 2 : (x - 1)^{2} (x^{2} - 4 x + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

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

The solutions are

x = 1, x = 2 + 2, x = 2 - 2

x^{4} - 3 x^{2} - 70 = 0

- 10 n^{3} - 15 n^{4} = 5 n^{3}

x^{8} - x^{6} - 2 x^{2} + 2 = 0

z^{4} + 27 z^{2} - 324 = 0

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

What are the solutions to the equation x^4-6x^3+11x^2-8x+2=0 ?
The solutions to the equation x^4-6x^3+11x^2-8x+2=0 are x=1,x=2+sqrt(2),x=2-sqrt(2)
Find the zeros of x^4-6x^3+11x^2-8x+2=0
The zeros of x^4-6x^3+11x^2-8x+2=0 are x=1,x=2+sqrt(2),x=2-sqrt(2)