What are the solutions to the equation x^4-6x^3+10x^2-6x+1=0 ?

The solutions to the equation x^4-6x^3+10x^2-6x+1=0 are x=1,x=2+sqrt(3),x=2-sqrt(3)

Find the zeros of x^4-6x^3+10x^2-6x+1=0

The zeros of x^4-6x^3+10x^2-6x+1=0 are x=1,x=2+sqrt(3),x=2-sqrt(3)

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x^{4} - 6 x^{3} + 10 x^{2} - 6 x + 1 = 0

x = 1, x = 2 + 3, x = 2 - 3

Decimal Notation

x = 1, x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

x^{4} - 6 x^{3} + 10 x^{2} - 6 x + 1 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 4 x + 1 = 0 : x = 2 + 3, x = 2 - 3

The solutions are

x = 1, x = 2 + 3, x = 2 - 3

0 = 4 x^{3} - 48 x^{2} + 84 x - 39.6

(1 - y) (3 - y) (6 - y) = 120

3 x^{5} - 4 x^{2} - 3 = 0, 0 \leq x \leq 2

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

x, x^{3} + y = 5

What are the solutions to the equation x^4-6x^3+10x^2-6x+1=0 ?
The solutions to the equation x^4-6x^3+10x^2-6x+1=0 are x=1,x=2+sqrt(3),x=2-sqrt(3)
Find the zeros of x^4-6x^3+10x^2-6x+1=0
The zeros of x^4-6x^3+10x^2-6x+1=0 are x=1,x=2+sqrt(3),x=2-sqrt(3)